Yes, the nozzle and nozzle cap work together as a pair. On just about every modern airbrush today, the nozzle cap is designed to be screwed all the way on when in use.
The Neo is an interesting brush. It has one of the smallest gaps between nozzle cap cap and nozzle on the market. This allows the brush to operate fairly well at lower air pressures. But, this also prevents it from being able to respond to higher pressures - they just never make it out the front without being reduced to a fraction of what you have set. This makes getting your paint reduction correct a key element of finding success with the NEO. Instead of upping air pressure, I would set up at maybe 25 psi, add a drop of paint to the brush, and then a drop of reducer or water - test spray to check performance. If it is not flowing, add another drop of reducer or water - repeat. Now, every color can be a bit different, and some will flow well right away. Some seem stickier than others, and may require a little more reduction.
Be patient, and try to learn what the bursh is really doing when it does or doesn;t do what you want it to.