Yes. you still need a cummerbund or a vest. No, the cummerbund does not have to be the same color as the pants. In fact, theoretically, it should match the tuxedo facings (the lapels) as should the tie and will typically be satin or, more rarely, grosgrain. There are such things as midnight blue cummerbunds but they are not strictly necessary for a midnight blue DJ. They may arguably be better, assuming the facings are also midnight blue. Since you are wearing a black tie, wear a black cummerbund as well. This is especially true while you are wearing a white DJ.
The fact that you are wearing a DJ for a tropical wedding is slightly disturbing as these wedding are typically much more casual. This wedding isn't happening during the day or on the beach is it?