Yes you will be changing your watches at some time but probably AFTER St. Marten and St. Thomas. They both follow Atlantic Standard time so are the same as Eastern Daylight time during the summer. During the winter there normally is a time change on Sunday night to AST and another one later in the week back to EST.
You won't change your clocks till after St. Marten and St. Thomas. If I remember correctly it's on Wednesday night (Thursday morning 2:00am) after St. Thomas to get you on Eastern Standard Time. It will probably be one of the most painless switches you've ever had since the day after will be a day at sea.