I’m pretty sure that the problem is unrelated to Music Studio and that the other IAA apps receive the MIDI signals directly from your keyboard.
In the other IAA apps, please try to disable MIDI input from all sources except Music Studio.
To test if it’s related to Music Studio, create a new project (save your previous one first!), with just a MIDI track and without IAA. Then manually open the other apps from the home screen and play on your external keyboard. If the other apps make a sound, they received the MIDI signal directly from the keyboard.
In general, Music Studio doesn’t reroute signals unless you active “MIDI Thru” in the Setup.