"The domesticated generations fell from him" means that Buck is losing his civilized characteristics (B).
In this passage, Buck is feeling more and more estranged from where he and his ancestors ("generations") originally come from: as he gets a taste of wild life, he feels less and less like a pet ("domesticated") and more like a feral dog or a wolf. He is forgetting his stay-at-home ways ("fell from him") and sees new instincts grow in him, such as the drive to fight and hunt in a pack.
