From the paper:
"
2. Lock Race Attack
In a lock race attack the sender forms two transactions and two locks and
submits one to the merchant and the other to the rest of the network. In this
case the locks will cancel each other out and the transaction MUST wait for
block inclusion before being considered confirmed.
"
So in the face of a simple double spend attempt, ZeroTime is no better than any other coin, it still needs to comfirm the transaction at least once with a Pow/Pos block.
This says if someone attempts a double spend they will have to wait for a confirm , zerotime still works to those using it for its purpose, only those trying to purposely double spend transactions are excluded until it is confirmed. so nothing really wrong there, you try to cheat the system you get temporary restrictions to the network. I.E not being able to use ZT for those transactions