Are you using the air cap guard when you spray those fine lines? It should be removed when you get in close to the model as it causes turbulent air flow. Be careful though, the Omni needle is easily bent.
Also, are you thinning your paint in the paint cup or outside the paint cup? I usually mix in the paint cup, but I find that when I need thinner paint, I get better results when I mix outside the cup. Perhaps I am not mixing the paint adequately when I mix in the cup, and mixing in a separate container get me a more homogenous mixture and more consistent results.
If that doesn't change anything, get back to the basics. Check your needle and nozzle for damage (use as high magnification). Make sure your parts are clean, etc. Out of curiosity, were you able to paint decent fine lines with your cheap airbrushes?
From what I see in the picture, it looks like your atomization isn't adequate. That is, you need finer droplets. The usual solution to that is add more thinner.
Check out Don's airbrush tips on pinting fine lines. He mentions the Omni 4k in his post-script, so it might be helpful.
https://sites.google.com/site/donsairbrushtips/fine-lines