different side of the clock, time zone

How should I correctly write the following?

The users are in different time zone and the server is in U.S time zone.

[about a game]
If you can take care of the camp on that side of the clock, I'll make you leader. [The person who said this lives in USA. When he sleeps I am awake, so while he's sleeping he wants me to take care of the camp]

Is it the way to say : on that side of the clock

Is time clock what they say?

I'm on a different time clock. When you get up I go to sleep.

Thank you in advance