Here's a scenario to explain what happens:
Object has a synced int.
Player 1 takes ownership of object and sets the synced int to 5. Everybody else sees 5.
Player 2 takes ownership of object and sets the synced int to 10. Everybody sees 5 turning into 10
Player 3 takes ownership of the object without changing anything. Everybody else sees 10 turn into 5, and then a moment later it's back to 10.
This is not an issue with precise timing, as it can happen even if the object has been 10 for several minutes. Somewhere, player 3 remembers that the object used to be 5 and it is interpolating into 10 or something, even if syncmode is none.