So I don't know anything about Bijoux Jewellers, but I was in Tortola and, with the blessing and advice from the "Shopping Assistant" from the Fantasy, I bought a ring at Diamonds International. What I paid in U.S. dollars for this "Tax free/duty free" ring was what it was worth in Canadian dollars. ie: it was appraised at 25% less than I paid. On top of that, I did have to pay duty to import it into Canada. I will also say that our Shopping Assistant advised against claiming it, which I think is bad for business on her part. I don't know her, so why is she encouraging me to break the law? Oh yeah, to seal the sale.
So, my advice is to beware of shopping in any of those places at the port for high-end anything unless you know what you're talking about. So if you're looking for something specific and you know the prices and you know your product, go for it. If not, maybe shop at home.