For either they or their even more confused pupils, unauthorizedly and erroneously, had then themselves gone and started baptizing not just "in" but even "into the name of John" (after he had pre-deceased them). Compare First Corinthians 15:29. It was, then, some of their heretical pupils and 'baptizees' in turn — that Paul later encountered at Ephesus. Acts 19:1-3.
Very strongly, however, did Luke (in his inspired Book of Acts) identify true Johannine baptism121 with the later 'Christic' baptism. By the latter, we mean that administered in the Name of the Triune God and upon the authority of the Lord Jesus as the Central Person of the Trinity.122
Very strongly did also Paul wish to underline the unrepeatability of all triune baptisms. So, he later reminded the saints in that same city of Ephesus that there was indeed only "one baptism." Indeed, there is only "one God and Father" and only "one Lord" Jesus Christ and only "one Spirit" — into Whose Triune Name all Christians should be baptized, even with water.123
Thus, at Ephesus, Paul gave trinitarian baptism "in the Name of the Father and of the Son and of the Holy Spirit" — for their first time ever — to these recently converted ex-unitarians. Such, then, apparently, were previously altogether ignorant of the Spirit's very existence (and perhaps even of Christ Himself). Such would themselves priorly have been initiated probably with water — but only "in John's own name" or, worse still, "into the name of John."
The latter initiation rite, of course, was not Christian baptism at all. It was not Christian baptism, precisely because it was not the same as the Johannine baptism which Jesus Christ Himself had received. For Christ received true baptism — on behalf of all Christians everywhere. Thus: Irenaeus;124 Hippolytus,125 Lactantius;126 Athanasius;127 Basil;128 Gregory of Nyssa;129 Augustine;130 and Calvin.131 So too Post-Calvinian Calvinists — like those who wrote the Dordt Dutch Bible;132 like Kuyper;133 and like Rev. Dr. R.W. Dale134 etc.
As Paul himself wrote precisely to the Ephesians: