I haven't been on the Eastern since April 2002. But, back then,
they did it the morning you arrive in St Thomas, no one can go ashore until everyone has cleared immigration. They have a very good system. They fill the rows in the theatre and then feed these people into lines to show appropriate documents. So first come, first served. They do this because you are re-entering US territory afoter being out of the country in St Martin. If anything has changes since we cruised, people will correct this.