I don’t know about Emma, but I think the “real world” definitely has magic. Remember how Regina killed the sheriff? She wasn’t anywhere near him and then she took a heart out of a box, and squeezed it until Graham (??? that was the sheriff’s name, right?) passed out and died.
Perhaps when Bae came to the “real world” there wasn’t any magic. However, when Rumple created the curse, in order to keep everyone here and keep everyone from remembering their true selves some magic had to be transferred over in order for it to work. So, now our world has magic even if it didn’t before.
(That’s the only way I can see Bae getting transferred to “our world” and “our world” having magic after he was already here)