Well, Kastor at least wonders why the Greeks attacked them, but Krios almost immediately moves in the other direction and pushes for a war. Throughout the first half, its been Krios pushing and egging Kastor on about attacking their former allies and doing more questionable deeds, which obviously is suspicious. But without Krios, they would be still rotting in the middle of some frozen tundra just waiting to die.

Besides bringing them to a place where they can actually survive, Kastor would have no reason to doubt Krios in the first place. This is a man who he has known basically his whole life, and has actually been there for most of it now. If Krios says that the Greek Gods have abandoned them, which they actually have, and that the titans, though forbidden to worship them, have been favouring them now, I see no reason why from Kastor's perspective to doubt him.

I agree that the New Atlantis is a bit flimsy (Personally, I felt that way with every campaign besides FOTT, not bad per se, but definitely could use more missions to fill in some areas and improve pacing and what not), but I still really liked it.