On the 'my games' page, you can see the time and date that you last moved. If you click on the game 'Info.' you will see two graphs that shows how much of the time bank is remaining.
So you can figure out when the T/O period will expire. When that happens, the Time Bank will start to be used.
If a move is not made before the time bank reaches zero, you will be given the option to claim a 'time out victory'. (A skull icon will appear next to that game on the 'my games' page.)
If your opponent does move before the time bank reaches zero, their time out period will be reset to the agreed number of days, but the time bank does not reset. It will remain where it is.
Does that help?