Moonrise 3:21 p.m.
Moon transit 8:36 p.m.
Moonset 1:57 a.m. on following day
Phase of the Moon on 5 October: waxing gibbous with 66% of the Moon's visible disk illuminated.
First quarter Moon on 3 October 2011 at 11:15 p.m. Eastern Daylight Time. ..."
The Sun and the Moon transit times are given for a particular latitude and longitude. That's what your professor is talking about. Those are the times the centers of Sun or Moon cross the central meridian.
This site may be more helpful:
http://www.usno.navy.mil/USNO/astronomic…
The world webpages do NOT adjust for daylight saving time. The Naval observatory just hasn't gotten around to updating the computer code for the world-sites. The United States web-pages didn't used to adjust for DST either.