@mika The video looks as expected to me, the hair moves a lot as the head is moved into a different pose without any mix transition. Do you mean that you want less movement of the hair, or do you mean that you don't want any movement at all when changing to the selected-by-cursor animation?
If you want less movement, you might want to set the Physics Constraint's Limit parameter in your Spine project to a lower value.
If you don't want any movement at all, you could reset Physics Constraints by calling Skeleton.UpdateWorldTransform(Physics.Reset);.
