I'm not gonna spend a lot of time on whether there was indwelling or outpouring, that's just me. The apostles got baptized and were given super powers. Not me. I don't know if you remember, but I was baptized once as an infant in a Catholic church, IMO a pointless act. But 1 billion Catholics believe you can't go to heaven without that, so you baptize a baby quick in case it dies.
I don't feel a need for another baptism, but one I day I might get off my lukewarm ass and do it.
So who does the baptism? A saint? And what is a Saint? Opinions vary:
1. Born again Christians believe that they are all saints. All go to heaven.
2. Jehovah's Witnesses believe 144k saints go to heaven. The rest of us, a great multitude, are resurrected for an eternal life on a Paradise Earth.
3. Catholics figure the Saints are on some list kept in Rome. They don't really believe in hellfire, so they have this Purgatory thing going.