I dont think the Fm9/G should be described as III13. I have encountered this before but I don’t know if I reported it.
SC3.07 Standalone / M2 Studio / Sonoma 14.7.4
Hard to tell what is going on there but in Dorian that should be a Abmaj13/G hence the III. I’m more interested in why it’s showing as a note out of scale. If you change the Scale to F Minor it will prolly make more sense in your example.
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@davide Heres another example where the F ranges from V to iii to II in SC3.1. My understanding is I am working with variations of the V chord in A#/Bb Lydian, all of which contain scale notes and all of which maintain the V root. They should all maintain the V function in the chosen key. And I am a novice so my understanding could be way off! 
I notice this happens when Voice Grouping is engaged. (Lots of great changes in 3.1 btw.)
