The other countries getting involved was to stop worse from happening.
From what I know about that war it was basically something that was bound to happen the moment Tito kicked the bucket. He was - like Saddam Hussain in many ways - the person that kept the spring-loaded component parts in an iron grip which some mistook for stability. Once the counter force was gone the various parts flew apart and started a war to try to gain the upper hand.
In Yugoslavia you could say that there never really was stability, only a temporary lack of opportunity to continue the fight.