There's a lot of evidence that Jacques and Alvin are not truly the same person. The only thing that attests to a connection between them is his stating back to Geralt what he says to Alvin on those occasions and what the King of the Wild Hunt says before you kill Jacques. He tells you that you knew Jacques de Aldersberg's soul by another name, not Jacques himself. I think that some kind of reincarnation explanation is most likely. They are both a source (the result of being the same soul perhaps, though this idea of reincarnation isn't much explored in Witcher lore in general), but to me Alvin looked up too much to Geralt and Jacques is too condescending toward him for them to be the actual same person. It's possible that Jacques reiterating Geralt's points to him is some nagging hint in his being from being the same soul. However, it's just as likely that Jacques's unrivaled magical abilities let him simply look into Geralt's mind and know what Geralt told Alvin. The entire Ice Plains sequence is an illusion Jacques conjures up, and he's clearly flat out lying to Geralt. He talks about it being the future, and yet there are skullheads. According to the bestiary entry, skullheads are an extinct animal, but Jacques is claiming they are the end result of human baseness in those who survive the frost.
He is obviously trying to pull the wool over Geralt's eyes, or he actually thinks he is an idiot, not sure. In either case, it obviously doesn't work.
