The current version of GarageBand saves projects under ~/Music/GarageBand by default. and iMovie uses an opaque "iMovie Library" in ~/Movies. I'm not sure about older versions, although from a quick Google it seems unlikely to me that it used those directories.

Apple's documentation[1] implies that applications are not supposed to use the documents directory themselves (only when the user selects it in the file picker).

[1] https://developer.apple.com/library/content/documentation/Ge...