The purpose of distilled water is to prevent build-up of mineral deposits in the chamber of the machine which will then shorten the operating life of the chamber. Using the tap water at the resort for the length of a vacation would likely not cause any damage to your machine, particularly if you clean it good with some vingar to remove any deposits when you get home.
A friend of mine that uses a cpap machine was making a trip to Guatemala to adopt a child and someone at the place she buys her supplies gave her a tip about her mask you may or may not find useful, they told her to save one old mask and use it on the trip and then throw it away when she got home. I can't recall the reason...build-up, or increased risk of bacteria? Water in Jamaica is certainly cleaner than Guatemala but just thought I'd throw that out there for consideration. You could ask your supplier what the rationale might be and if it would be of benefit for you.