FF6 Enhanced soundtrack

Yeah, pretty much that. The starting volume is just for the very first note, then the fades dictate the volume, both increasing and decreasing. Usually I would also re-set the volume after the fade down, so it has a starting volume before fading up, but here that is not the case due to how the song old lady part sounds (fading up from silence), so it is fading up from 0 to 64 and then down to 0, in that example I showed.

edit: the starting volume though doesn't have a direct impact on the fades, other than it will either be closer or not from what it is fading to, but for some reason it seems to have done all the fades wrong somehow in the song you have linked, since it seems to be extra quiet.