I'm not the one making the claim, but found something that this tall tale might be based on: https://www.grunge.com/756660/the-mysterious-bay-of-jars-explained/

Tldr: Brazilian entrepreneur throws some amphorae into a bay to grow barnacles on them for aesthetic reasons. Disreputable sea treasure hunter finds some of those, makes a flurry of wild claims, gets banned from Brazil for theft of actual antiquities from another wreck and he goes silent when people start asking more questions.

So the closest I came when looking for a source, was 20th century amphorae in a Brazilian bay, nothing about a roman shipwreck in the Carribean. But since the claim was a roman "galleon", a claim for it to be in the Carribean also means little.