On my February Anthem 8 niter departure in Nassau was 4PM and at 4:30 we were still anchored. I kept seeing passengers some walking and some taking their sweet time, with not a care in the world. Crew and officers kept the chattering and communicating with the Captain, Finally, at about 4:45 everything was pulled up and with the drama over headed to the dining room.
Next stop was Coco Cay, so they had some flexibility.
In this instance, don't know if those tardy Paxs communicated with the ship's authorities.