An hour ahead at the airport in Tobago is probably fine, but I always plan to be there 90 minutes ahead of the departure time.

I use ATMs when I travel with my normal ATM card - NOT a credit card. A credit card makes you pay interest and fees right away.
I use my regular ATM that is linked to my credit union checking account in the states - absolutely no different than being at home - except the amount you enter for the withdrawal is the amount of the LOCAL currency.
I get a good exchange rate through my credit union and pay no fees whatsoever.
So, I now usually only bring a couple of hundred dollars in cash with me and use an ATM when I need more.
If you are not sure if your card will work, take extra cash or travelers check this trip, and try using your card and see what happens.
The credit card can always be used as a last resort.