We just completed a NCL cruise out of San Juan. We saw this happen at almost every stop. They are very clear about the time you have to be back aboard. The ship typically leaves the port 30 or so minutes after that time. They expect you to be embarked by the embarkation deadline they communicate, not the time the ship leaves the port. Those names you hear being called over the public address system just prior to leaving the port? Those are the people who weren’t registered via check in by room key as embarking.
Overall we are reasonably pleased with NCL. The food in the dining room can be hit and miss. I had some great meals and some dismal meals. However if you don’t like what you ordered, you are welcome to order something else-and you should. As for the buffet lines, sure there are some things that are not good. But there is always a large enough selection if you look across all the lines that you can find something that you like. One night they even had Beef Wellington on one of the buffet lines during our stay.