No. As the recent June/July 1996 Blue Moon illustrates, a slight difference in time zone can spell the difference between whether the exact moment of Full Moon happens on one day or the next. Astronomers define the moment of Full Moon in terms of Universal Time which is the local time relevant to citizens of Great Britain. If you live at a longitude 90 degrees west of this, you clock is set to a time zone that is 6 hours earlier than Universal Time. This means that if a phenomenon occurred at 3AM on July 1, you would observe it at 9 PM on June 30. This isn't a relativistic effect, just a consequence of living on a BIG planet!