The game is tied to the server, not to your client, you will not see the ability being used until the server has recognized it, it is actually a step in the right direction as far as competitive purposes go.
Try this, go to a friends house, use an ability, and see when goes off on yours and his screen. It will be at exactly the same time. (in wow you would see about a 1.5 second delay based on latency)
It takes a bit getting used too, but the end result is actually more synchronization with the server.