I take joy in exuberantly pushing back on their insistence of clinging to such archaic time units as "minutes", "hours", and "days", telling them to come back when they embrace kiloseconds. It is telling that most of my friends accept this with equal joy and laughter (:
It probably doesn't hurt that I've also spent time drilling metric conversions so that I can code-switch pretty seamlessly among units. Neurotic tendencies can have payoffs.
That doesn't make it unusable as a cross galactic time unit, and I think the same goes for years and hours.
(... it's not exactly pi-squared because the French yanked it around a bit before settling into the modern number based on light in a vacuum and cesium atoms).
Currently, a Mars days is called "sol", FWIW.
If we find other species out there I won't speculate on how they think about time.
I don't think that helps with the original concern.
"Our dates start x trillion rotations of pulsar y ago and our unit is defined as z wiggles of cesium" is a starting point.
But you can tell an alien species our units are expressed in multiples of that, and they can translate it into how theirs works. (Vinge, for example, has space-faring humans talk about "megaseconds" and "gigaseconds" rather than days/years.)
More like weeks and decades. Arranging to meet someone in a megasecond is like meeting them on the weekend; a megasecond is ~11.5 Earth days. A kilosecond is short enough to be used for moment–to–moment planning. They’re about a quarter of an hour each so they’re good for scheduling work tasks, scheduling time to meet people for a meal, etc etc.
Gigaseconds are more rarely used, since each one is ~32 Earth years.
Diaspora by Greg Egan has some fun with this too. The main character is a software emulation; called a citizen rather than a flesher. Most emulations live at a subjective rate 800× faster than the flesher normal. The second chapter is three flesher days after the first but 256 megatau, or ~8 years, have passed for the main characters. The fourth chapter is two thirds of a teratau later, over 20k subjective years. For the fleshers of Earth a mere 21 years have passed. The main character has actually forgotten the events of the third chapter; one of his friends brings it up and he has to search his archived memories to figure out what his friend is talking about.