His holy men made it so. One of them confronted Blaze on the Pit 2, to bring him to guard this egg as I recall.

Yeah, it's not blatantly stated out-and-out, but the implication is that his holy men did some rituals and whatnot that tied Onaga's soul to the egg. Which allowed him to basically not go to the afterlife, and instead he could hang around and do things like appear to Shujinko as a ghost calling himself Damashi and possess Reptile when the egg hatched and all that.