The International Space Station is in a different gravitational field than us on the Earth's surface. Almost all computers / protocols depend on the Unix epoch being consistent everywhere. The Unix epoch is same for all computers on the Earth's surface, since they are in the same gravitational field. Do the computers on ISS need to be corrected for the difference in gravitation field and epoch changed likewise.
POSIX time doesn't include leap seconds, and is not implemented the same way in every UNIX, so it routinely gets inconsistent for several seconds every couple of years. It is not a high-precision time scale, and there is little point correcting it for relativistic effects which are smaller than it can represent. GPS has to be corrected --- in particular, the clocks have to run slow on the ground, so that they speed up to the correct rate once in orbit --- but GPS clock errors are measured in nanoseconds, and GPS satellites orbit much farther away than the ISS. Time-based network protocols have to be much more forgiving of errors, or their false alarm rate will be too high.
It doesn’t yet matter for most practical purposes. The slowdown from faster motion and speedup from a weaker gravitational field partly cancel out, and the net effect is that time on the ISS is only 0.0000000014% slower than time on Earth, so in its whole 22-year history it has lost about one hundredth of a second.
Computers on the ISS do not rely on UNIX/POSIX time, they rely on GPS time.
Broadcast time is the time broadcast from ISS computers that is intended to be indicative of current time.
The broadcast time message is with respect to the GPS time scale, not the Universal Time Coordinated (UTC) time scale.
The time is accurate to ±1 s:
Due to various reasons, the C&C [command and control] computer clocks are allowed to drift with respect to the Spacecraft Integrated GPS/Inertial Navigation System (INS) (SIGI) time by up to ±1 second. All other ISS computers sync to the C&C computer.
...but can be corrected to ±55 ms:
The GN&C [guidance, navigation, and control] computer calculates the time error of the C&C computer as compared to the SIGI GPS time and provides that time error in Broadcast Ancillary Data (BAD) data. The time stamp of each data packet can be adjusted by adding the time error to create a time stamp that is accurate to within ±55 microseconds.
This is according to the External Payloads Proposer's Guide to the International Space Station (SSP 51071).
Unix time is (sloppily) based on UTC, which in turn is based on TAI (international atomic time). TAI is a coordinate time, an implementation of TT (terrestrial time) defined to be equal to proper SI time of a stationary clock at Earth sea level, and extended to be synchronous everywhere in Earth-centered coordinates.
Even clocks on the Earth's surface must be corrected for altitude to match TAI. Clocks on GPS satellites require a much larger correction. GPS time is kept synchronous with TAI as accurately as possible.
For precise timekeeping on the ISS, we use GPS time, so precise ISS clocks do not tick at exactly one second per proper SI second. For example, the NICER pulsar instrument uses a sloppy (100 ppm) clock in each measurement unit, but calibrates the clock against GPS once per second, thus achieving accuracy of a few nanoseconds relative to TAI after processing.
Just to have an idea of the order of magnitude:
"Time dilation explains why two working clocks will report different times after different accelerations. For example, time goes slower at the ISS, lagging approximately 0.01 seconds for every 12 Earth months passed."
Similarly, between Earth surface (1 g) and Mars surface (1/3 g), so time goes faster on Mars by things are faster on Mars than on Earth by 555 seconds per 1e12 seconds on Earth (1e12 seconds on Earth is more than 31688 Earth Years!). So you will be celebrating Earth New Year a tad earlier on Earth than on Mars, but Martians won't care, they'll celebrate Mars New Year!
The gravitational field doesn’t matter for practical purposes- computers’ performance isn’t measurably affected by gravity. What might be measurable is that the ISS is travelling faster (certainly in terms of ground speed) than terrestrial computers. However, the Earth isn’t stationary but is orbiting the sun, galaxy etc and so (a) the difference may be very small, and (b) if you use the ISS as your frame of reference then it’s stationary and the Earth is moving. Either way, having CD a few seconds of drift either way isn’t generally a problem for communications.