I'll only give a small overview if this:
Or do deep space exploration probes need this in general?
Inherently, they don't - but often they do perform time synchronization, or clock re-calibration.
The clock on spacecrafts is a counter, often maintained in software, derived from a hardware oscillator. An absolute(1) (earth) time can be derived from that counter when we know when it started and the period of which it is incremented. So time on the spacecraft is a relative time, just a counter from when it was started. (This is conceptually the same as how time is kept on a normal PC).
Now, all oscillators drift, the counter wraps around, and there's other problems with this kind of timekeeping, but carrying atomic clock for timekeeping is normally infeasible on spacecraft.
However, as long as one knows the value of the onboard clock (the counter), when it was started, how much that clock has drifted, all data is available to calculate the time.
Calculating the absolute (earth) time can be done by ground systems derived from the relative timestamps of data from the spacecraft clock to earth time. Commands sent to the spacecraft can be translated the other way, from the absolute time used on earth to the future relative time used on the spacecraft.
Ofcourse, the translating to/from earth time to the spacecraft time can be done onboard the spacecraft as well instead of on ground systems - in such cases
periodical time synchronization is needed so correct time can be maintained. Correct time in this case can conceptually just be to transmit the current absolute time to the spacecraft, and have it maintain the difference between that time and its onboard counter, so it can just add an offset from the onboard clock to get the absolute time.
Whether absolute time is kept on the spacecraft or the ground system depends on the spacecraft and mission - often both are done in order to ease and prevent errors in timekeeping from coming up. In either case telemetry from the spacecraft about the onboard clock, its value, whether it has been reset, overflowed, and other parameters are very important.
(1) Ofcourse, the "absolute" time we use is really also a relative time from an epoch and according to some more or less arbitrary calendar.