Buck creates a "mutiny" by first building credibilty amongst the other dogs (and his masters). He proves himself to be a leader for the good of the group, not simply for selfish purposes. The other dogs recogize this in him. Once Spitz (the antithesis of the type of leader Buck becomes/is) is defeated by Buck, the other dogs accept Buck's ascension to the leadership position.
As the story progresses, the stage is set for a positive leader to assume the helm. The dogs have toiled under Spitz's heavy-handed leadership. It's all they know, so they acquiesce. It's not until they "see the light," i.e., Buck is introduced to the team that they realize Buck's potential to lead them in a more positive, productive way.
Buck seems to sense the needs of the greater good. Both Francois and Perrault realize his potential as well. They let things play out as they know they should. They know that it's only a matter of time before the two types of leadership philosophies come into conflict. The two must battle it out and I think that they welcome Buck's victory.
This same victory could not have come had Buck not proven himself (through his actions). The other animals, witnessing his leadership, were willing to let Buck lead.