I know people from the US like to play their cards close to their vest but end up paying dearly for it. There are not a lot of secrets on the island and you may be the only one who is not in the know. You have not said what property you bought nor who the caretaker is. I have watched other gringos be totally shocked when they find out there little enterprise was known to everyone except them - then they were surprised when they learned the hard way.
Your place is going to be vacant.
Security is esential.
Your grounds will need to be tended on a very regular basis or it will quickly be overgrown.
The plants will need watered - sometimes even in the rainy season.
Repairs will need to be made after every storm.
If you have beach front it will need raked not only for appearance sake but to keep down the sand flies.
Remember - you get what you pay for.
Like was said above - have a sit down - listen - and keep everything pretty much the same for at least six months.
In the meantime read "Don't Stop The Carnival" and between belly laughs pay close attention to the reality.
I live here and I love it and would not live without a caretaker - and get a dog.