There's typically a central time source sending a 1Hz pulse into the main computer(s). The sensors will use something like Time Triggered Ethernet, RS-485, or a MIL-1553 bus.
Yeah this is in line with my experience. However there are concerns about the accuracy of quartz clocks as temperatures fluctuate, this poses a problem for some orbital patterns.
Thanks to both answers - I've asked couple engineers of my generation and "that would be an interesting concept" was the best response I got. I have so much to learn!
For LEO missions, the source is now typically a GNSS receiver outputting a PPS line. Otherwise, you try to have a precise clock (TCXO, OCXO, and now CSAC are available) as a reference distributing the time to all the subsystems, and you correct the satellite time offset from the ground (similar to NTP).