Since the place you are staying is not on the approved list, you will be required to quarantine at the property for 14 days. You will be required to record your temperature daily and you may be called or visited by the Ministry of Health.
Getting through the airport will be the easiest part. You may want to stop and shop on the way to Negril because once at the property, you will not be allowed to leave it or visit with anyone for 14 days.