This is actually an interesting question. How is age handled in a space-age civilization? Someone born on one planet could be 10 while on a different planet they'd be 50 in the same timeframe. What if you spend part of your life on one and the rest on another? It'd be inconvenient to use one planet's 'day' as the standard, as they'd all be different lengths...
One would believe an atomic clock to show the same time in seconds despite the celestial body it orbits. Though, that appears to be a fallacy and begs the question, what about relativity? Two identical atomic clocks would show different times depending on the influence of gravity (like near-lightspeed travel), so does everyone carry a clock around with them?
Or, at least that's what I remember from physics class.
You could pick a neutral thing and then denote that as the galactic 'clock'. We do it as humans to an extent. We use Pulsars to measure distance and time because of the extremely precise rotation times.
Either that, or we'd just use UTC, still. Like on the ISS or Mars. Bet you computers in that timeframe would be hard built on earth's and society's system.
We just need yo hand waive things like time being relative.
There's no universal clock keeping time.
Think Interstellar, but that it would apply to an entire galaxy since people move at different speeds and live in different places and time runs differently.