Werner,
We were on the 12/13 Eastern and the immigration/customs process was just as you described. The process at debarkation was very quick. I know they can ask you to open your luggage for inspection but I didn't see anyone being asked this when we went through.
Also, another note on St. Thomas day. On our cruise, only the people with shore excursions had to be at immigration at 6:30 am. All others went from 7 - 8.