While his mistreatment at the ASZ is a matter of fact (most often initiated by Rosita), that would not be enough for Eugene to join the man who forced him to witness the murder of his friends. That would make Eugene utterly devoid of any moral fiber--a walking parasite. I don't think Eugene falls into the parasite category, so he's trying to play Negan for as long as possible.
Would Eugene consider anybody in Alexandria friends, though? Although it was shitty for Eugene to lie about needing to get to Washington because he had the cure for the zombie virus, I can see why he did it because he's unable to survive on his own. Nobody in the group ever looked at Eugene the same way again and treat him like garbage for the remainder of the time at ASZ. In fact, he's not even given any meaningful tasks to do. The only thing he does is wander around on the verge of tears all the time while everybody (namely Rosita) berates him.
While the Saviors (namely Negan) show appreciation for Eugene's solution to the rotting zombie fence problem and reward him accordingly. Instead of feeling like an outsider, Eugene finally feels like he has a place (and a good place at that, being higher in the food chain than one of Negan's other grunts).