If you book through the cruise generally you get off the boat first, and they will let you know when you need to exit the ship.
If you book on your own, then I would check with the tour operator, find out where the pickup or starting point is, and how long it usually takes to get to their location from the boat.
If you book on your own and need to tender in (like in Grand Cayman), remember that you may not be allowed to take a tender until all the ship booked cruise people have gotten ashore. This can cause you problems if you have a morning tour planned.
Another note about GC sometimes, (more than you would guess), that ship passes it by due to rough seas. If you book there on your own, make sure you check the refund, canceling policy of the tour operator.