By arranging to act simultaneously, they placed themselves in the same reference frame.
BTW, could that IRF be described as "approximately SunTime + [(1/c) X 1AU]" ? '-)
Regards!
To be more accurate, I suppose that position would have to be defined including the date to derive relative motion between earth and sun, since the earth's orbit is not circular...
But, you are correct -- inasmuch as I had to refer to position (relative to the Sun, whch has its own [constantly changing WRT the Galaxy center, etc.] position)...
Of course, by convention, "earth time" is measured at the Prime (Greenwich) Meridian. Your watches merely indicate your angular displacement (± 7.5 degrees) from the Prime meridian. Again, as you point out -- position...