Other games wouldn’t matter, as it would have to work on a per-game basis, simply because the hour timers would drift off of the on-the-top-of-the-hour timeframe.
If you restart the game, then you’ll start with the current Terror Zone with the current on-the-hour timeframe the server has selected… Which means you’d have the option of rerunning the current hourly Terror Zone, or rolling through the next random Terror Zones that come after the current one is cleared.
The “next” Terror Zone that comes after a clear of the current TZ would be completely random, so no.
Lets say you are on the first random Terror Zone change after clearing the current active server Terror Zone, the top of the hour comes, your game would not be affected and the current Terror Zone would continue to run its course for the remainder of its hour time frame or until you meet the requirements for another random TZ to come. Again, it would be on a per-game basis. However, if you restart the game, then the Terror Zone would be set to the one the servers have selected along with the current on-the-hour timeframe that is set.