Kompany's problems with Mancini started when he went to see him over something Mancini was doing which the players weren't happy with. Vincent made a constructive suggestion and Mancini basically told him to fuck off and mind his own business. Vincent wasn't impressed, particularly as it was done in front of the other coaching staff.
From what I've heard about Pep, he would have listened, explained what he was doing and why and, if Kompany's suggestion had any merit, might even have incorporated it. If not, he'd have told him why.
Also Zab was another who had his say about Mancini and he's still there. I really don't think it's anything to do with that, more with their attitude since then.