I think they need only to check if the coins reached on the deposit address on both chains. Then these coins are safe. It doesn't matter then which chain will win since they have the bitcoins on both chains.
Huh?
You are not making sense. An exchange is going to on one fork or the other (not both unless they want to be giving away fiat).
If your exchange decides on Fork A and then Fork B finally wins out then that exchange will go "belly up" (as all the coins it has had deposited would be unsalable).