Barbados cherry is native to various islands in the West Indies in the Caribbean. It has become naturalized in southern Florida and Texas in U.S. Department of Agriculture growing zones 9b through 11. That means Barbados cherry is sensitive to low temperatures.
Mature trees can tolerate only brief periods of exposure to 28 degrees. Cold protection is required if you grow them in Mississippi. My home garden is in zone 9a, so I’m going to grow mine in a big container in case I have to move it inside to avoid a bout of cold weather.