Typically in first person shooters that use controllers, you get controller vibration when you fire your weapon, its a form of feedback that's supposed to make you feel like you're really firing a weapon. Most games do have an option to turn off the vibration feature though.

Yes, most games have the rumble feature and the ability to turn it off. Unfortunately, Arma3 is lacking these features, including the ability to customize the button settings.

I leave my controller plugged in at all times, it vibrates when I shoot or drive/fly a vehicle even when i'm using a keyboard and mouse, I only use it to fly and do not want it vibrating all the time making noise. please resolve.