Expanding the Network Time Protocol for interplanetary use:
[...] The current NTP technology has no provisions for mobile servers and clients, where range and range rates can vary with time, and only minimal provisions for intermittent connectivity. In the Mars internet, orbiters and surface stations may have only intermittent connectivity, while in the DSN segment real-time connectivity is possible only at scheduled opportunities and then only with very long delays. These considerations are mitigated by the fact that ranges and range rates can be predicted with some accuracy from the known positions of the spacecraft bus, orbiters and surface stations using ephemerides maintained by astronomical means.
[...] It may will happen that residual clock frequency offsets may introduce considerable error if the time between updates is relatively long, as would be expected during communication opportunities between Earth and mission spacecraft. After a few measurements the frequency can be disciplined in the usual way, but this affects the position and velocity vectors and residuals with respect to the ephemeris. What makes frequency-induced errors more nasty is that the frequency may fluctuate due to spacecraft thermal cycles and power management.
And from the article:
Relativistic effects (in the solar system when not in a black hole) are nearly irrelevant when compared to the errors from (a) NTP clients moving at up to 60 km/s and (b) clock frequency fluctuations due to heat changes and power management. Assuming they're using quartz crystal based clocks, those vibrate at a given frequency when a given amount of energy is applied; voltage fluctuations throw them off and changing the ambient temperature throws them off; most other ways of measuring time have similar issues. As far as I'm aware, all current methods of keeping time have potential issues with heat. And don't discount that whole relative movement thing (okay, that's what the whole "| Tp - Tp(i) | < Tp * (V / c)i+1" equation is about); NTP isn't exactly good at dealing with latencies that change in that manner. Besides, NTP calculations should already deal with relativity; if your computer clock has a consistent drift (say, loses one second every ten minutes), the NTP server on your machine will notice after a while and automatically correct. This is no different than if you have a different amount of gravity and therefore a different rate of time and as they said, they want everything on the same timescale off of the atomic clock.
I *think* that they're taking into account the Special Relativity effects, but not the General Relativity effects. I'm sure it won't matter on timescales of a few hundred years, but a clock sitting on the Earth will run slightly slower that a clock free falling in space near the Solar system.
One of the retired professors here at the University of Arizona was responsible for the GR corrections for GPS systems - if you didn't take into account the blueshift of the GPS radio photons falling down to your receiver, they can't triangulate to better than a kilometer or so.
Anyway, as the article says (and you pointed out) you're not using NTP for better than millisecond time keeping.