We stayed there before our November cruise. I think we had three shuttles going to the port. They had our names on a list for each van. We were sharing the shuttles with Norwegian cruisers. We were let off at the Norwegian ship and had to walk with our luggage back to the Magic. On the way to the port the driver passed around a paper that told us which pick-up space and when to be there. We went to the space a half an hour before the pick-up time and one of the shuttles was loaded already and left. We waited until about 10 minutes before the time on the paper and another van came. We loaded up and waited until 10:30 (the pick-up time). A family of 5 came at the last minute and the van was one seat short. Luckily one of the kids was small enough to ride on a parent's lap. No one else came to the pick-up spot, so I assume that one of the vans came much earlier than the scheduled time.
It was pretty cold outside or I would have been at the stop earlier. Just be sure to get out there with time to spare. It was just too much stress for me at the end of our cruise. There were plenty of parking spaces available at the terminal when we embarked. If we cruise out of NYC again, I might consider an uber ride or parking at the port. By the way we drove from Ohio.