Yes - when screwed down there should be sufficient pressure to create a seal between the connections. It should not move.
Also, check the tube itself. I had a C02 leak which I thought was a bad o ring, but the tube was actually dented/damaged.
Replace the o ring - test it
If you have another keg switch the tube using the new o ring - test it.
If it's still leaking at that point you might have the threads on the hex nut or actual keg that's damaged.