I'm not sure if they turn them off exactly, more it is a product of where they are. The infinity stones are about controlling the universe, but at the TVA they are effectively out of the universe so have nothing to control.
It's like if you took your TV remote out into the middle of a field away from your TV at home. You haven't stopped your TV remote working or being a TV remote, it just hasn't got a TV to effect.
They also have so many as I suspect they are often involved creating timelines that they have to prune, so they become useless trinkets.
It's no coincidence that the one they had the most copies of was the time stone