Private tours are never affiliated with the cruise lines. If they had booked their tour with the cruise ship and the tour was running late, the ship would have waited. The rules are made clear. Also, the ships need to leave the ports by a certain time, no exceptions.
Correct me if I'm wrong but there is a limit to how long the ship will wait, because as you said the ship has departure deadlines. However, if the excursion is affiliated with the cruise line, arrangements will be made by the cruise line, at no cost, to get the passengers to the next port of call.