So my experience was from 2016, no clue if it has changed at all.
We didn't have the UBP this time, so we went to Publix and bought eight bottles of wine. When we got to the port, after security, we were directed to a side table where a staff member tagged/numbered our bottles of wine and charged us $15US per bottle. That's it.
We would bring a bottle to dinner each night, no questions asked.