Obviously, this idea assumes the latter. Now you may ask, “Are there time zones in Olam Habo?”.
I don’t know the answer, but perhaps it follows the time zone of where the person is buried, or where he died, or where his descendants live. Or perhaps, the length of time out of Gehennom depends on how long Shabbos is kept in one area regardless if it’s at the same time.
A reason given for the minhag that an avel does not lead the tefillos on Shabbos is that it gives the appearance that he considers his parent a mechallel Shabbos, and therefore in need of the zechus to save the parent from Gehennom even on Shabbos.
We don’t find that if the son is in a different time zone, that minhag changes, nor do we find that he doesn’t lead Erev Shabbos Minchah or Sunday Shacharis because somewhere in the world it’s Shabbos. The son’s Shabbos is apparently representative of the parent’s, even if not actually aligned, so that concept may very well apply to the inyan of tosefes Shabbos as well.