Earth already has this problem. Years aren't consistent both because the number of rotations don't evenly go into a single revolution, but also because Earth's rotation time is variable. For instance, above normal fresh water accumulation on land will measurably change the length of a day.
Generally, there are two solutions. One is to track absolute time by increasing the clock as necessary to realign the day to the year. There are Earth days with where the last minute of the day is 61 seconds long. Daylight Saving Time makes days with 23 hours or 25 hours. And, of course, leap years add a day. Unfortunately, a lot of software/hardware is built by people with misconceptions about time, like a minute can have only 60 seconds or a day can have only 24 hours.
So, the second solution is to update the system periodically. Computers often poll internet time to update the clock and will jump to the new time. Alternatively, some systems skew the system clock with additional milliseconds per second until it catches up with the time change. As long as the values are valid typical ranges, most software doesn't care about sudden changes.
Generally, there are two solutions. One is to track absolute time by increasing the clock as necessary to realign the day to the year. There are Earth days with where the last minute of the day is 61 seconds long. Daylight Saving Time makes days with 23 hours or 25 hours. And, of course, leap years add a day. Unfortunately, a lot of software/hardware is built by people with misconceptions about time, like a minute can have only 60 seconds or a day can have only 24 hours.
So, the second solution is to update the system periodically. Computers often poll internet time to update the clock and will jump to the new time. Alternatively, some systems skew the system clock with additional milliseconds per second until it catches up with the time change. As long as the values are valid typical ranges, most software doesn't care about sudden changes.