A private tour is not affiliated with the cruise line. If they were on an official shore excursions the ship will wait. That is why ship board excursions are more expensive.
Here is a hypothetical; what should the ship do?
Both a ship's excursion and a private excursion are taking passengers to the same national monument (e.g., a Mayan ruin, Pompeii, etc.).
Both excursion transports are stuck in local traffic due to an unforeseen accident complicated by emergency vehicles and are delayed for 30 minutes while returning to the ship.
Both excursion transports arrive 30 minutes late to the ship at the same time.
Will the ship board only the ship-sponsored excursion passengers and deny the other passengers boarding, or will the ship board both sets of passengers?
-PJ