Those who booked excursions with the ship often are able to leave the ship first in a group. Also those in suites or high up on the loyalty program leave early, too when tendering is involved.
Yes,excursions are staggered and the groups usually meet in the theater. Some excursions are scheduled in the morning; others may occur in the afternoon. Occasionally, a few occur at night. Sometimes they meet on the dock. You excursion ticket will tell you where to meet and at what time. Be sure that you arrive 15 minutes prior to meeting time so as not to hold up the group.
How big the group is depends of different factors: how big the port is, the size of the vehicle, or how many people sign up for the tour. The nature of the tour may also diswtate the size of the group. This would probably be listed in the tour brochure as limited participation. Sometimes there may be multiple vans or buses on the same tour.
How quickly passengers can get off the ship depends on how quickly the ship gets cleared by the local authorities. Sometimes this can be further delayed by passport problems of passengers or crew. Sometimes mechanical problems with the gangway may be a problem or even strong winds could delay disembarkation. Usually, though, it is the clearing of the ship that determines when passengers disembark. .