Sorry about the delay. I'm usually offline all day Wednesdays.
I do have an iPhone and use CarPlay regularly. I agree, it's not getting the time from the phone. It's also not getting it from my home internet.
Although I don't have an active subscription, the car usually tells me, either on the screen on over the speaker, that I have limited OnStar service. It looks like that means Vehicle diagnostics, Dealer maintenance notification, Smart Driver, and Marketplace. Don't know if that helps with the clock.
I might leave the clock on auto for a couple of days and see if it gets better. I did not get the Navigation or the Roadside Assistance services, so the GPS may or may not be active. The cell tower location makes most sense to me.