You shouldn't have to turn the water off but, if the valve sticks (which your one apparently is doing), then water will run back and out of the filter.
No mains water comes into the appliance until the valves are open for drinking water and/or water for the ice maker.
The water that comes out is simply the water in the tubing going from the filter to the drinking water spout.
Hope this helps
Let me know how it goes