Here's the content of the letter I received for my December Millennium cruise:
ABOUT YOUR UPCOMING TRAVELS
We look forward to welcoming you aboard the Celebrity Millennium® for your 14-Night Southeast Asia Holiday sailing departing from Hong Kong on December 07th, 2019. Before you embark on this exciting journey, we would like to share some important information.
Each country on your sailing will have unique immigration requirements. Please be sure to contact the embassy or consular visa services of your choice for specific visa requirements, information, forms, and fees as these differ by nationality. It is the responsibility of each guest to identify and obtain all required travel documents for the entire cruise vacation. Please note that guests who do not provide the proper documentation at check-in may be denied boarding.
For your convenience, we will collect all guest passports after departure immigration clearance in Hong Kong, in order to complete the immigration formalities on your behalf in each port of call. Your passport will be held in a safe location at Guest Relations on board and will be returned to you when all procedures are complete.
Again, we look forward to welcoming you aboard Celebrity Millennium® for a truly incredible vacation. See you soon.
It looks to me like you have to apply for your visa before you board the ship.
Hopefully, it is an easy process 🙂