(TL;DR; It sounds like the joystick device is broken by design?)
I googled a bit around and found other users with the same problem (this time with Steam):
https://steamcommunity.com/discussio...0549123317909/.
I'm not sure what happens. It sounds like (perhaps?) the firmware on the joystick tries to figure out "who" is trying to use it based on usage, and possibly reconfigures itself when it thinks an Android device is using it, for compatibility with Android? That's just a theory. If so, it could be a matter of "luck" whether an application's usage of the device triggers this (undocumented?) functionality in the device.
Anyway, I don't know if I can do anything about it. I'm simply using the SDL2 library to use joysticks, and apparently, this is not an FS-UAE-specific problem.