Leo,
I got in played around on your test site a bit today without being able to recreate the issue at all. I can see the one user you mention who has duplicate fields, but I tried the following scenarios, and in both cases, my profile was imported normally and without duplicates.
The first time I tried to register, I ran into a few minor redirection issues. I fixed this by going into the "Extensions" area of AceSEF and telling it to skip JFBConnect. We only have 1 url page for JFBConnect, so this isn't a big deal. After that, I did everything below and it worked normall:
1) Registered a new user through Facebook. In this case I was redirected (after creating my account) to the "Verify Information" form which was blank. This confused me at first, but I realized this wasn't my JomSocial profile... after going to my JS profile, my information was all there including my avatar.
2) Then, thinking that maybe it was an issue with associating a 'new' Facebook user to an existing account, I deleted the above user.
I then registered through JS normally.
I logged in, to check my (empty) profile.
I then logged in through Facebook and used the left-hand form to login with an existing Joomla account
My profile was imported and everything was normal.
I'm not sure where I'm going wrong (or right), but if you can test and recreate the issue, that'd be great. Did this only happen with that specific user one time, or has it happened multiple times? Obviously, it shouldn't ever happen, but I just can't get to the bottom of it.
Hopefully, it was just the SEF issue, but let us know what you find and we'll help however we can!