I mean, genies can be bound with those bracelets which I'm guessing were made by some kind of magic.

We were discussing this at katieliz's; within the metaphysics of the movie, it doesn't seem to be so much that genies are bound by some magic as that bondage is the native state of geniehood, as when Jafar becomes a genie the bracelets automatically reappear as part of the whole package.