Augustine is an interesting case because being in North Africa, he did not need to depend upon faulty Greek translations of letters of events happening in his back yard. He probably had access to some of the original autographs of the actual letters. His retelling of the events is crucial, because it gives us the insight of a saint into an issue in which he had the actual sources at his finger tips.
When reviewing Augustine’s historical analysis of the rebaptism controversy, On Baptism-Against the Donatists, Book III is our best resource. As follows are quotations from this book and my analysis:
…in even earlier times, Agrippinus, or Cyprian himself, or those in Africa who agreed with them, or any others in far distant lands beyond the sea, were moved, not indeed by the authority of any plenary or even regionary Council, but by a mere epistolary correspondence, to think that they ought to adopt a custom which had no sanction from the ancient custom of the Church (par 2).
Clearly, Augustine concedes that the North Africans were rebaptising during the third century, something that he asserts “had no sanction from the ancient custom of the Church,” meaning there was no prior custom (i.e. the position of Pope Stephen I.) Whether this is historically true appears unlikely, being that the concilliar documents have always taken a middle road between Stephen and Cyprian and they include rebaptism. Nevertheless, this fundamentally is Augustine’s position. Augustine’s own argument, that Cyprian’s position was an innovation, is particularly poor:
Or how, again after the time of Agrippinus, when, unless there had been a return to the primitive custom, there would have been no need for Cyprian to set on foot another Council (par 3)?
In short, the idea is “if rebaptism is the original custom,” they would not have had to have more than one council on it. This is like saying because Nestorianism was condemned by Ephesus I, Chalcedon, Constantinople II, and Constantinople III then Nestorianism must have been the original custom of the Church because if it were not so many councils reiterating its condemnation would be unnecessary.
Augustine is positing that at the time of Agrippinus, rebaptism was introduced, then “the prior custom” came back, and then Cyprian held a council to reintroduce rebaptism. This is a silly argument, as councils reiterate doctrines and practices all the time without the wrong practice being reintroduced or vice versa. However, it makes sense for Augustine to make this argument for polemical reasons, even if it is tenuous.
Augustine is working with no different source material than what we presently have available to us today. For example Augustine writes:
For Cyprian himself says: “But some will say, ‘What then will become of those who in times past, coming to the Church from heresy, were admitted without baptism?'” Whether they were really without baptism, or whether they were admitted because those who admitted them conceived that they had partaken of baptism, is a matter for our future consideration. At any rate, Cyprian himself shows plainly enough what was the ordinary custom of the Church, when he says that in past time those who came to the Church from heresy were admitted without baptism (par 7).
The clear argument that Augustine is asserting is that Cyprian’s 72nd epistle concedes that chrismation without rebaptism was the original custom. However, if we look more closely at that letter, Cyprian says nothing of the sort.
While Cyprian does view Pope Stephen I’s position as an antique but corrupt custom that had crept in at some point (Epistle 73, par 9), in his letter to Jubainaius (Epistle 72) he asserts that he expounds a prior North African custom of very good authority:
[I]t is no new or sudden thing for us to judge that those are to be baptized who come to the Church from among the heretics, since it is now many years and a long time ago (par 3).
Cyprian then proceeds throughout the same letter to show that from the Scriptures, the North African custom was the original one. This makes sense when both sides assert custom and there is no solid historical evidence to decide which one came first. In evaluating the Roman custom, for example, Cyprian writes:
[W]e cannot find that any one, when he had been baptized by heretics, was received by the apostles in the same baptism, and communicated in such a way as that the apostles should appear to have approved the baptism of heretics (par 13).
Nevertheless, Augustine employs the same biased historical interpretation in his parsing of the Council of Carthage (approx 258):
For in the Council itself Castus of Sicca says: “He who, despising truth, presumes to follow custom, is either envious or evil-disposed towards the brethren to whom the truth is revealed, or is ungrateful towards God, by whose inspiration His Church is instructed.” Whether the truth had been revealed, we shall investigate hereafter; at any rate, he acknowledges that the custom of the Church was different (quoted in par 8 of Augustine’s work).
Augustine claims that Castus decried custom and in so doing conceded that the North African view is an innovation. This is untenable for several reasons. First, decrying a custom is not the assertion that one’s own position is not itself customary. That’s an argument from silence. Second, we in this council have appeals to rebaptism always being the custom of the North African church. Donatulus of Capse asserts that “I also have always thought this.” Munnulus of Girba said, “The truth of our Mother the Catholic Church, brethren, has always remained and still remains with us, and even especially in the Trinity of baptism.” Third, at the council “the letter of Jubaianus written to Cyprian had been read as also the reply of Cyprian to Jubaianus,” and so they would have heard the appeal in that letter to North African custom.
Additionally, Novatus of Thamugada writes that “according to the testimony of the Scriptures, and according to the decree of our colleagues, men of most holy memory, that all schismatics and heretics who are converted to the Church must be baptized,” making a clear appeal to the antiquity of Agrippinus’ council. Nemesianus of Thubunae asserts that the North African position is universal (contrary to Augustine’s claims): “All these things speaks the Catholic Church.”
This does not mean that there was not a “sola scriptura” streak among some of the council fathers. Felix of Bussacene said, “In the matter of receiving heretics without the baptism of the Church, let no one prefer custom to reason and truth, because reason and truth always exclude custom.” However, Augustine’s point, that the council shows that they had a new teaching over against custom is incorrect, because we have too many indications that they were appealing to Catholicity and previous custom on their own behalf.
Why does Augustine, in some sense, tarnish Cyprian’s legacy? Cyprian was, afterall, a rebaptizer. Augustine had no problem conceding that Cyprian rebaptized wrongly (the position of his Donatist opponents), because this demonstrated that Cyprian prized not entering into schism more than rebaptism:
If I am unable to gain my point, and show how those arguments may be refuted which they bring forward from the Council and the epistles of Cyprian, to the effect that Christ’s baptism may not be given by the hands of heretics, I shall still remain safely in the Church, in whose communion Cyprian himself remained with those who differed from him (par 2).
…neither Agrippinus nor Cyprian ever deserted, nor those who agreed with them, although they entertained different views from the rest of their brethren…Cyprian himself, for he declared that he remained in communion with those who received heretics and schismatics, and so also with those who were received as well (par 3).
Cyprian, indeed, says that on this subject not one, but two or more Councils were held; always, however, in Africa. For indeed in one he mentions that seventy-one bishops had been assembled, — to all whose authority we do not hesitate, with all due deference to Cyprian, to prefer the authority, supported by many more bishops, of the whole Church spread throughout the whole world, of which Cyprian himself rejoiced that he was an inseparable member (par 14).
The final passage aforementioned is odd as it asserts there was a worldwide council that decided the issue. It is probabl that Augustine is referring to Canon 7 of Constantinople I (which shows the North Africans received its canons). Canon 19 of Nicea I indicates that Paulianists are rebaptized, but makes no mention of conditions where people are not rebaptized. It is possible Augustine is citing something apocryphal, but based on the evidence we have, Canon 7 of Constantinople I makes the most sense.
The interpreter of Augustine must choose one or the other possibility. The latter invalidates Augustine’s view of history and custom pertaining to this matter. The former suggests that Canon 3 of Constantinople I was likewise accepted in Africa if they were citing the canons of Constantinople I as authoritative and ecumenical. It creates issues for Roman interpreters either way.
Ultimately, Augustine asks good rhetorical questions (par 17) that suggest Cyprian was the innovator, but in so doing he reveals he has no additional insight into Cyprian than the letters he cites. He may have never read Saints Firmillian or Dionysius of Alexandria. He probably never read Pope Stephen I, as he refers only to what he gleans from Cyprian’s letter (Book V, Par 31). As a result, Augustine’s assertion that the custom of not rebaptizing (and thereby Pope Stephen I defended the original custom of the Church) is simply an assertion. It bears little historical importance to the question at hand.

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Met. Kallistos of Diokleia
Some fifty years before Cyprian, the same view had already been expounded by another African writer, Tertullian, in the De Baptismo (a work belonging to his Catholic period, probably composed around 198-200): For us there is one, and only one Baptism, since there is only one God and one Church in the heavens… But the heretics have no participation in our teaching: the very fact that they are excluded from communion proves them to be outsiders… We and they do not have the same God, nor the one — that is to say the same — Christ; and so we cannot both have the one Baptism, for it is not the same. (De Baptismo, 15)
So Tertullian draws his conclusion: since heretics do not possess the one Baptism, they lack the power to confer Baptism on each other.
https://classicalchristianity.com/2014/07/06/on-cyprianic-and-augustinian-theories-and-heterodox-sacraments/
I find the baptism controversy in North Africa to be so interesting, since really it all started due to the question of pastoral discretion from the 3rd and early 4th centuries.