I understand why it does indeed sound like you're performing multiple actions from a single button. But as you've rightly concluded yourself, only a single action will be performed, simply because the first available ability will get triggered and the game won't handle anything more until the next time it's ready to receive input after that global cooldown - which you'll have to press another button for, because all other input is discarded, the same way it would if you'd press multiple keys simultaneously on a keyboard with your fingers.

So the end result is that by pressing one button, you are still only executing one action per character, and you'd have to press yet another button to have your character do anything else, so there is no automation involved.