The Rivers family I’m related to, were all from England and established themselves on the east coast of the US around the time Columbus discovered America. They were tobacco plantation owners who had many slaves. Often the slaves took the sir name of the plantation owners, ie. Rivers.
Maybe the Rivers in Jamaica had already been to America, escaped,and were going back? Not sure though.
Where does your Aunt live in Ca.?
All of my more current family originated from South Carolina. Do a Google for Rivers in South Carolina.