Digimon Story: Time Stranger (disc version)

Am I just dumb? I thought I'd be able to continue with my demo save data via the full game? Or is that only for the digital version? It seems ridiculous...

I read that a pop up asking if you want to continue with save data should pop up but my only option seems to be to start a completely new game.

I'm connected to the internet and as far as I know, I am updated to the latest patch version... ;_;