I didn't anticipate something like that happening... Sorry about that! I'll look into it to see if there's a way to fix it.
Viewing post in Isla En Moratoria - WebGL Version comments
I run into this problem with unity games periodically. (At most with simple game, and rare for last half-year)
It's very annoying to pull-out joystick dongle from PC to play another game on itch.io, when joystick itself can be even without batteries.
Just win behavior(I saw same with an another models, mostly wireless) + unity have lack of start calibration.