Since the Zanarkand that Tidus and Jecht came from was basically being produced by the Fayth, it's possible that through some kind of subconcious thought the sound of the hymn was recognisable to all of it's citizens. Plus it's made clear that Tidus has knowledge of some of Yevon's customs (the Blitzball victory stance in Zanarkand is a sign of prayer/acknowledgment for Yevon).