If it really is a 10 minute adjustment, and not 10 seconds, that is worth checking out. If it were only 10 seconds, I wouldn't have suggested that it was only a lag adjustment.
You should write in to support after the game. Use the help and support contact link which is on the bottom of every page. Report the game ID and the details of what happened.
From your description, this must be when you are playing on a phone app, since you don't have to leave the main board to message an opponent on a normal web browser. Be sure to provide the details of what app/browser you are using, how many times this has happened, etc.
I would think that this should happen when you are watching as well as when you aren't. Your opponent doesn't know when you go off the main board.
There are certain flaws in Live Play that may please be addressed.The opponent's Clock is suddenly jumps from what is displayed by 10 minutes ie., from 3 minutes to 13 minutes when We go off the main board to send messages to the opponent.