What they think will happen is that it will be picked up by a "loop current" which flows southeast from the mid Gulf of Mexico and then meets up with the big "Gulf stream"- which flows from the Caribbean northeast towards Europe so it will be carried away from the Caribbean.
. . . .
But by the time it crosses the Atlantic ocean it will be so diluted with much of it sinking or evaporating that it isn't expected to be much of a problem there. The biggest threat is to the keys and southeast Florida where the Gulf stream runs close to the coast.
Of course, as with hurricanes, the exact path varies with weather conditions and is subject to change.