I don't think there was anything heavy handed about it at all. Coyle made his decision and let the staff go to begin seeking new opportunities. The assistants don't need their hands held and rather than keep them in limbo he set them free. Enlightened and generous.
And this is not how it is done at most programs. Usually the staff is retained until the new coach is hired then it is up to the new coach to decide who stays or goes. This was heavy handed.