The concept of leitmotif goes back as far as Wagner, most likely further. So it makes sense that the character's theme helps us to connect to the character, even if they're not present using musical cues. A great example of this is the Imperial March, which first appeared in the Empire Strikes Back as a stirring musical backdrop to the might and power of the Galactic Empire but has appeared in pretty much every movie since then to represent Darth Vader and his tragic story. Hearing it while watching a sweeping vista of Star Destroyers is very different than hearing it when meeting Anakin as a cheerful child.

Aerith's theme has popped up in expected places. I once heard it played on clarinet during a church service. Since the musician was a teenager I'm guessing he didn't think the adults would notice the source but of a course I did. So it works in new ways even beyond the confines of the game.