A lot of these mobsters were trying to diversify into legitimate businesses. Just like Reno and Las Vegas, a lot of these mobsters invested in gambling resorts in Cuba.
When communism came, not only did they have investments that wanted recouping, they had valuable contacts on the ground and firsthand knowledge of the area. So the c.i.a. and these mobsters had common interest and things they could do for one another.
As to how they got in touch? I don't think they were hard to find. Hard to prosecute maybe, but by and large they were known.
Even today there are descendants that still claim they're owed reparations from the Cuban government.