If a module is "arduino compatible", does that necessarily mean it isn't compatible with other microcontrollers?
The term "Arduino compatible" basically means nothing.

Many sellers use the term more as marketing ("You can make this work with your Arduino!") than anything else.

The Arduino is (usually) just an ATMega microcontroller on a board, that ATMega is very similar to many other microcontrollers. Nearly all of them work with a supply between 2 V and 5 V as does the Arduino. If a peripheral also works within that supply voltage range (and almost all of them do) then you could call that peripheral "Arduino Compatible". But it will work with almost any other microcontroller just as well including your PIC32.