I am also a jazz musician.
this scale:
C# D# E F# G# A B C#
is C# Aeolian.
Minus the A natural, that is one collection of notes that is being strongly suggested by this app. Yes, an A# would would change the tonality, and the key.
To me, I hear the 9th scale degree relative to the tonic much more than the 6th (i.e. 13th). That's in general, and it's based on my own predilections and harmonic training. This scale includes a D#, as well as the 4th and 5th. I "hear" this as relative to C#, not G#. Totally welcome, of course, that you hear this as relative to G#; the E natural then functions as the minor 6th. To me, that's a much weaker harmonic suggestion than the E natural functioning as the minor third. It's totally OK with me that we hear this differently. Is it OK with you?
Also, why does it matter to you what I (some random person online) realizes (or not)?