The thing is the game inputs must keep synced "per frame". If There is a delay of only one frame between the inputs in two consoles, the game will begin desyncing more and more. Which is what happened to us.
We noticed there was the obvious lag, but we thought the lag was because it synced the inputs in both consoles.
But it turns out it's not syncing them well.
Also, if you want both games to be perfectly synced from the start, the only way to make sure everything is the same in both games is to send one savestate at game startup, so both games are perfectly synced. If not, some random events could be different.