The available time in a multi-player-game starts with the time limits, that the game was set up with. While in setup-mode, the time is not running down. The clock starts to run only after the game has been started by the game-master.
 
The remaining time is separately counted for the Black and White color. If Black is to move next, the Black time normally is counting down except for the following conditions:
 
If the game was started with the weekend clock stopped, then the colors clock is not counted down on weekends. This is independent from the players, because the weekend-clock is based on the GMT timezone.
 
If the current Black player has to move next, the time counting down depends on the characteristics of the particular player, that fulfills the Black players role at that moment (colors may change for Zen-Go). Is that particular player on vacation or in his sleeping time, then the Black time is not counting down. Similar applies for the White color.