How does the cell phone know where the state line is?

I was driving the other day between two states – Alabama and Georgia. The state line happens to be the demarcation point between the Eastern and the Central time zones.

I happened to have my cell phone in my hand, and just as I got to the state line – like, within 50 feet of it – the time on my cell phone changed from 3:00 to 2:00 (I was going west).

I know that most cell phones get their time set by signals from the cell towers; that makes sense. But how can the towers know that I was at the state line? Is there GPS working in here, too?

(of course the clock on the dashboard did not change – which is a pain)