Do all people from jamaica or any small island always show a positive tuberculosis test?

TB test: The PPD test is only positive if you have been exposed or if you have had the vaccine called bcg. The bcg wanes over time and probably doesn't protect you anyway. If PPD very positive and bcg was many years ago then you probably were exposed and need to be checked - next step is a chest x-ray.

Only if immunized: If immunization was in effect on that island (cuba immunizes against tb), then the skin test will be positive. You need to know that information in order to interpret the skin test results of anyone from any of the islands. I don't know if immunization is in effect on all the carribean islands.

No: There are several tuberculosis tests in the U.S. A skin test (ppd test) can be positive if a person has gotten the TB germ into her body, or has had a bcg vaccine. Rarely, one can have a positive skin test from exposure to germs that look like TB germs but are not the real TB germs. If a skin test is positive, one can do the quantiferon gold TB blood test to check for real tuberculosis exposure.