Technically it’s not how it happened in the book IIRC. Nobody was throwing corpses into that well. Just stones. And it wasn’t in the hall of Mazarbul. It was in some guards’ room near the gate.
Their entry into Moria, bothering the nice guy guarding it, was enough to wake the Balrog.
It works the way that the happy tentacle owner and Balrog and Orcs were working together to exterminate Balin’s expedition.