Paul explained baptism to the unbaptized unitarians
This is why Paul now explained,92 to those ignorant unitarians at Ephesus, the nature of the true Christian baptism which John himself had indeed administered. "Then Paul said: 'John truly baptized with the baptism of repentance, while saying to the people that they should believe in Him Who would come after him' — that is, in Christ Jesus" the Spirit-anointed One.
"When they heard [and heeded] this, they were baptized into the Name of the Lord Jesus."93 This could mean that Paul did not baptize them at all, but simply told those men that John himself had indeed baptized people into the Name of the then-coming Messiah — that is, the Lord Jesus. Thus: Calvin, Beza, Wolleb(ius), the 1637 Dordt Dutch Bible, Georg Calixtus, Lightfoot, Budde, Rambach, Gravemeijer, H. Hoeksema Sr., and others.94
On the other hand, the above Scripture could also mean that after those men repented — Paul now baptized them into the Name of the Lord Jesus. This would then be because, as former unitarians, they had previously never been baptized by John at all — and also never yet in the Name of the Lord Jesus Christ as God the Son (and indeed as quite the Central Person of the Holy Trinity). Thus: all the old versions, the Syriac, and Jerome's Vulgate;117 Abraham Kuyper Sr.;120 and myself (Francis Nigel Lee).121f
Yet either way, there is no re-baptism at Acts 19:5. Indeed, it says there: "they were baptized." It does not there say that they were re-baptized.
The fact is, according to Luther and Calvin — and all Classic Lutherans and Classic Calvinists — 'Johannine baptism' is 'Christian baptism.' Thus, on this identification specifically in this very passage Acts 19:1-7, nearly all Calvinistic scholars. See: Calvin, Beza, Wolleb(ius), the 1637 Dordt Dutch Bible, Lightfoot, Cocceius, a Marck, De Moor, J.H. Heidegger, J.H. van der Palm, H. Heppe, Gravemeijer, A. Kuyper Sr., H. Hoeksema Sr., etc.95
So too, apparently, also the great and godly Lutheran Rev. Dr. Rudolph Stier. He rightly states96 there is nothing said about re-baptism in Acts 19:4-7. Those who had been baptized by John the Baptist, were not — at the beginning of the evangelical preaching — ordinarily baptized again with water. See Acts 1:5. But here in Acts 19:5f, in the case of those who were already removed and estranged from the proclamation of John, it was needful that the law of the Kingdom should be maintained and attested by their new baptism. This was their first-ever Christian baptism, right then administered by the Apostle Paul. Thus Stier.
The text could thus mean that Paul was here informing those men at Ephesus about what John himself97 had really taught. This would then show that those who had heeded John's preaching — namely John's preaching that they should believe in Jesus — were there and then baptized by John into the Name of the then-coming Messiah (Jesus Christ). In that case, after explaining this to the confused men in Ephesus, all that Paul then further did — after they had heeded him — was 'waterlessly' to lay his hands upon those ex-heretics.
Alternatively, Luke's words — "when they heeded this, they were baptized into the Name of the Lord Jesus"98 — may instead be referring to what those ex-unitarians in Ephesus next did in relation to Paul. This would mean that Paul himself then proceeded to give those ex-unitarians inter alia their first-ever triune water-baptism.
Perhaps Paul did not then give water-baptism to those men. On the other hand, to us it seems more likely that he did.99 Either way, however, the entire passage Acts 19:1-5 cannot properly be taken to mean that the trinitarian Paul re-baptized those ex-unitarians — after they had heeded his teaching. If Paul indeed baptized them with water — that would then have been the first and the only Christian baptism those previously ignorant ex-unitarians had ever received.