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Set your clock to Zulu time, it is never wrong. Then all you need to do is subtract your time zone hours from it. Example: Zulu Time - 5 hours = Eastern Standard Time. Set your clock to the 24 hr setting, makes the math easier
As everyone has figured out, the car clock needs to be reset manually. Your cell phone is automatic because the time is sent from the nearest cellphone tower.
What no one has mentioned is that you need to set your C6 clock twice- once for driver 1, then punch the memory button on the door for driver 2 and set the clock again.
My wife and I are sometimes on different wavelengths in the car, but never in different time zones.
If it has NAV the procedure is different. With ignition on go to the music notr under the source button with radio off. Touch the clock icon at the middle bottom of the screen. The rest will be self explanatory or just look under nav in your manual and look for time.
You can do a search on the internet for whatever year owners manual you want and it will come up in total. I use it all the time to keep from pulling out my owners manual from the rear storage bin since it is a tight fit for the glove compartment. Keep in mind that if you have Nav you must set it with the satellite having a view of the sky, And you must set it every 6 months as it is not like a mobile phone and set itself.