Notice how quickly the staff takes cover - the perp isn’t even through the first set of doors and already the tellers are hitting the floor. I wonder if the moron was announcing his intentions as he charged in - it that’s the case, he probably signed his own death warrant, as it gave the old guy enough lead time to draw and take aim.
You answered your own question -- somehow the tellers knew very early. Maybe they saw the gun, maybe he was yelling, maybe he was moving too fast, maybe all that, maybe more.
Note to self: when robbing a bank, don't hold the gun high in the air for everybody to see, and don't (probably) yell "this is a robbery!".