The food prices falling might actually result in a net negative impact on their economy.
If local producers can't viably compete with aggressively low priced American crops, they'll lose out heavily.
On the whole, the tourism will probably bring in a lot of money, but a good chunk of it would leave the island immediately, and they'd have to wrangle a flood of goods they didn't have to compete with before.
(A lot of Caribbean islands end up in situations where the major tourist hubs are owned by American companies that pay locals as little as possible and then ship the profits back to the US. So the island just sees the benefit of 40 jobs, not 200 high paying tourists a month)