Some of y'all have got John Gill, Wilhelmus a Brakel, Turretin, Calvin, Matthew Winzer, Ed Walsh, and Purely Presbyterian and who knows who else against you. As clunky as the language might seem in Acts 19:5 I think all those guys and others may be right:
John Gill on Acts 19:5-
"When they heard this..."
That is, the people to whom John preached, his hearers; when they heard of the Messiah, and that Jesus was he, and that it became them to believe in him:
"...they were baptized in the name of the Lord Jesus;"
Not the disciples that Paul found at Ephesus, but the hearers of John; for these are the words of the Apostle Paul, giving an account of John's baptism, and of the success of his ministry, showing, that his baptism was administered in the name of the Lord Jesus; and not the words of Luke the Evangelist, recording what followed upon his account of John's baptism; for then he would have made mention of the apostle's name, as he does in the next verse; and have said, when they heard this account, they were baptized by Paul in the name of the Lord Jesus: the historian reports two things, first what Paul said, which lies in ( Acts 19:4 Acts 19:5 ) then what he did, ( Acts 19:6 ) where he repeats his name, as was necessary; as that he laid his hands upon them, which was all that was needful to their receiving the extraordinary gifts of the Holy Ghost, having been already baptized in the name of the Lord Jesus: which sense is the more confirmed by the particles (
men) and (
de) , which answer to one another in verses 4 and 5, and show the words to be a continuation of the apostle's speech, and not the words of the historian, which begin in the next verse. Beza's ancient copy adds, "for the remission of sins".
(It also occurred to me that Apollos was apparently not rebaptized but only more fully instructed, though he had only known the baptism of John. Acts 18:24-28)
See also
https://purelypresbyterian.com/2016/04/24/was-johns-baptism-christian/ (Short article, quotes from a Brakel and Turretin).