The vaccine is making no changes in the requirements at the present time. From the Visitjamaica.com website:
**** IMPORTANT ****
All travellers who are 12 years of age or over, will be required to present a COVID-19 PCR or Antigen test that has been authorized by the United States Food and Drug Administration (FDA) under an Emergency Use Authorization (EUA) or meets the standards of the World Health Organisation (WHO), to the airline representative at check in. The date of the test sample collection must be less than 3 days from the date of travel.
A negative test result must be presented in order to complete check in for a flight.
https://travelauth.visitjamaica.com/