Time is not "relative" in the way you think; it is absolute. The "Big Bang" does not happen in one person's future and another person's past.
It is true that our year 1931 is in the future for people in 1900, and in the past for people of 1960, but that is immaterial, we just measure time from a fixed and arbitrary point of time in the entire universe, in our case AD 0, picked for no rational reason whatsoever.
The same thing goes for our years, days, hours, minutes and seconds: These are all arbitrary, picked for our own Earth-centric idiosyncratic circumstances. The same thing applies to our distances: A "foot" is the length of some King's foot, a cubit the length of some King's elbow to fingertip. But a "meter" is based on the circumference of the earth, divided by a power of ten, both of which are idiosyncratic to Humans or Earth, respectively.
If Martians did the same and all their names for time and distance were based on martian physiology, Mars or Martian history, we would (with examples) be able to translate.
So you embrace this arbitrariness. Pick some arbitrary points in time of your own, pick some arbitrary distance of your own, and treat time as a location being visited.
So say our arbitrary time is "days", and arbitrary starting point is AD 0, just like now. For convenience we standardize on metric prefixes: In powers of 10 for Deca, Hecto, Kilo (10, 100, 1000), and in powers of 1000 thereafter: Mega (106), Giga (109), Tera (1012).
About 3 decadays in a month. A hectoday is 100 days, a kiloday is 2.738 years, a megaday 2738 years, a gigaday 2.738 M years, teraday 2.738 G years. The Universe, at 13.8 G years, is about 5.04 teradays old.
Likewise we can pick an arbitrary point in time to measure from. Say AD 0 in our current calendar.
So the diary is a sequential series of entries, Each with a location: kday 875.4, Mars, Cairo Settlement:
Earth has 365.25 days per year, so translated, 875.5 kilodays is 2396.715 years, or day 261, in a leap year is Sep 17, 2396, Earth time.
The Time Keepers themselves wear a device that communicates with their home base. Their protocol is strictly periodic meetings, on some time schedule relative to the home base. Every decaday (10 days). The time keepers themselves age based on their location; on Earth, one day per day of the mission.
For convenience sake and to avoid confusion, they only return to home base on meeting days, to their own designated location there. But of course can communicate with each other from anywhere in the universe at any time. That perhaps creates causality paradoxes in Einstein's formulation, but we threw causality and Einstein's formulation out the window with time-travel in the first place. You really don't have to worry about Einstein's Relativity, because you have convincingly disproven it with Time Travel.