Unfortunately, the Second is measured for purposes of our timekeeping standards at sea-level on Earth which is ~1PPB slower than it would be in free space, as opposed to having a correction factor built into our time standards and so, for example, interplanetary ping times would be slightly shorter (in UTC/TIA nanoseconds) than expected.
I mean, than nucleus is much heavier and much smaller than electron, so it will be much less affected by external forces. We may see no difference between sea level and space based Thorium-229 clocks, or difference will be much smaller.
9,192,631,770 is clearly a sensible number and not something that's blatantly chosen to match some arbitrary pre-existing geocentric standard like 10,000,000,000 would have been.
It's retrofitted to what we already defined as a second, sure.
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.)
> "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.