Given a "Date Revision Due" for revised submission of a journal paper, am I required to submit before the beginning or the end of that date?
Unlike conferences, a journal's "date due" is rarely quite so precise a moment; this is because papers are all being dealt with asynchronously, on an as-arrived basis, rather than as a massive batch of hundreds all arriving near-simultaneously as for a big engineering conference.

Most journals will be comfortable with you submitting a little late if necessary (though there are some that will automatically discard your paper if you don't hit their deadline).  Thus, rather than fretting about time-zones, I would recommend that if you are worried about a last-minute submission, you instead email the handling editor and ask for a short extension.