Ok, I managed to solve it. It was related to make the infos public or not.
My main issue is this: I would like the user to be able to see his/her infos, but make them not visible from guests.
ok, I made it!
But now I am experiencing another issue; on the profile page, I just see the cover and profile pic.
Even if i link all the fields with ‘more info tab’, nothing appear.