Local input prediction won't work unless the player's inputs directly control the object and are also run by the host, as described in multiplayer tutorial 3. If the physics behavior is just simulating by itself without using player input, then it is inappropriate to use local input simulation.
For just syncing objects in general, it should not matter what behaviors you use. Simply run everything on the host, then on the peers disable all the behaviors and sync object will move them like they appear on the host.