No, the gasket should sit on the top, between the rim of the bottle and the carbonation cap. But they do have a bit of a habit of slipping inside the bottle if you tighten them too much.
I find I can get a great seal at 30-40psi without having to tighten it too much. Mine is just a cheap AliExpress carbonation cap.
Also the gaskets are normally loose, not held in place by that hex nut. You need to be careful the gasket doesn't get lost when not connected to a bottle, as there's nothing holding them in place.