Control animation blending by changing parameter at the right moment

In Mecanim I have a Blendtree with running animations in different directions. When I change the direction parameter onStart it lasts some time till the blending to the new direction is done, even without dampTime. What I want to achieve is that the blending is finished onStart, so the change of the parameter has to happen before. I want to do it with an animationEvent, but when is the right moment for the call? Is there a possibility to specify this exactly?