Syncing needs to happen before the object is spawned. Usually this is done on start of layout, and only needs to be done once.
For a card game, you don't necessarily need to use the sync feature. A more straightforward method could be to simply send messages between peer and host, and have events on both host and peer side to handle what happens when any given message is received. It will be up to you do keep the host and peers in sync in terms of what is shown, but this is relatively simple to check and implement in a turn based or card game.
I recommend you to actually follow and complete all four multiplayer tutorials until you can understand everything that is written on the multiplayer plugin's manual page. Implementing multiplayer isn't easy - it basically amounts to making two versions of your game that rely on outside (each other's) inputs.