For example, if it's 1:15 PM and 30 seconds on the Eastern seaboard of the US, I can be certain that it's some variation of X:15 and 30 seconds in every location on Earth. When did these times synchronize, and what was the driving force behind that innovation?
Not discouraging further answers, but this older answer from u/kookingpot may be of some interest.
Just to add a wrinkle, that’s not exactly accurate.
There are several time zones that are off by 30 minutes or even 15.
(So at your 1:15:30, it would be 10:45:30 in India, and 11:00:30 in Nepal)
Http://worldtimeserver.com gives a good list.