Tighting taps under kitchen sink doesn't cut off water supply
Those are supposed to be shutoff valves, but they are usually very cheap and I would not be surprised if the rubber washers are more like bricks.

If you need to do tap maintenance you will need to turn off the apartment's water. Unless you are in a condo this is really the building owner's job, not yours.

I stopped using this style of shutoff ages ago. You can get mini ball valves that are much better in every way for very small extra cost.