We get the time from the GPS and in the SOP's I have used for the first flight of the day is to check off the GPS to ensure the aircraft clocks were the same as that. I am sure newer aircraft have it auto sync to the GPS.
The area centers are always pretty much the same as that. Some towers though are out by up to 5 mins. Leads to all sorts of financial arguments when the airfield wants to charge for out of hours and the tower reckon its 21:01 and the weight on wheels in the FMC records it as 20:59.