I don't want to actually even imagine what sort of hell an proper interstellar empire timekeeping is. Just ignore different planets having different orbital and rotational characteristic.
Just the basic relativistic effects even with some type of instant transfers would make most communication and so on massively painful mess.
At least, we have a well-defined second. Assuming that humans make interstellar travel and/or colonization happen before being visited first, it's not entirely unreasonable that space-borne vessels will maintain the time and calendar system developed on Earth. It's convention, after all (we fudge it _just a bit_ here on Earth, too).
Perhaps extrasolar colonies will have to develop a system that makes sense for whatever planet or moon they settle on, at which point they'd be converting between Earth time and local time for correspondence.
Problem isn't that second isn't well defined. Just that the rate of seconds passing in well defined way depend on location of observer. We already average bunch of clocks around the globe. But doing the same thing light years from each other...
Just the basic relativistic effects even with some type of instant transfers would make most communication and so on massively painful mess.