Well, you have at least 2 problems here although the situation isn’t entirely against you.
Your first problem is that if the user only promised you 50 backlinks in the gig, the results aren’t actually usually the responsibility of the seller even if they use hype to convince you. If someone offers you 50 backlinks and they give you 50 or more backlinks (even really horrible ones) they’ve actually delivered as advertised. The seller doesn’t have to offer you a refund unless Fiverr forces them to or unless they offered something else that they didn’t deliver. Fiverr will sometimes back a seller in this case due to the gig wording.
In your own case, while you broke the forum rules by posting the username and it was removed, I can also tell you that the user appears to have been banned. That doesn’t excuse posting the username since neither buyers or sellers should be called out on the forums. The good news for you is that if the user was banned, they probably violated the Terms of Service or got a ton of complaints, so your feedback isn’t necessary since they can’t sell anymore. The other good news is that you’ll get your money back as Fiverr credit and you can use it to promote your site in a better way.
There are people who know more about this than I do, but buying general backlinks isn’t usually going to yield good results. What you want is promotion that offers some kind of really legitimate promotion. Someone who can promote your site on keyword specific forums/sites/blogs in one example. Someone who can do backlinks with strong proof of results might be useful. There is a seller in the UK who is a Top Rated Seller, does all kinds of SEO work and has thousands of good reviews.