Yeah, if the transaction is replayed on the fork chain, and the transaction signs for a utxo that doesnt exist over there, it's an invalid transaction. But honestly, splitting coins for BIP-110 is a pretty stupid thing to do, since it likely won't even have a spot market before the miners abandon the effort. Lot of room for error with very little chance of reward.

It'll definitely be disruptive, but it'll work out in the end. I'm not stressing over it.