DNA cousins reaching out

It's a DNA cousin explosion!  I kind of gave up on the requests that I've sent out to DNA cousins that have no response.  Now in the space of weeks, I have four share requests  --  two from Ancestry and two from 23andMe.  Two of the requests (one from each site) have strong Caribbean roots.  I vaguely remember whispers that we have family in "the islands" on my paternal side.  Here's one message that floors me because he can trace his family from the 1830s and I'm, just up to the 1870s as far as documentation.

"We appear to be related according to our DNA results and I was curious to know the connection.
My family has been based Jamaica since the 1830s.
Do you have any clues as to our family connections?
Kind regards
Ray"

I also have communication from a DNA cousin, who was put up for adoption at birth, with a very interesting story.  He's trying to find his biological connections.  Our connection seems to be maternal because his biological parents are from Ohio where I know many of my maternal family went to from Mississippi  --  but time & research will tell.  I am drawn to this request & almost feel obligated to find out if we are related so I can give him the sense of family that I always had.

At any rate, now I have to seriously step up my game to understand DNA connections.