The details of the lifting of the curse were engraved on the chest. The fact that there was a curse was known all along, presumably that information came with the compass. It was just that the pirates didn’t believe in the curse. Why should they? If you have a lot of money, of course you’re going to say you’ve got bodyguards with the eyes of hawks and booby traps and curses. It’s only as the curse affects them that they begin to “believe in ghost stories.”
(I think Jack says he didn’t believe in the curse when on the island with Miss Turner, but I haven’t a quote.)