People use the term dead zones with ambiguity so it's sometimes hard to diagnose, but my experience says its the module.
Can you use a small flat head screwdriver to gently pop one of the orange sensors off a unused cage, pop out the black circular wiper bit, and post a picture of the inside of the sensor? That will tell me if they sent you the wrong one.
As far as fixing it in software, no. If there is slop in the sticks, as per:
Stick at 0% (center), you push it up to +25%, let go -> it stops at +15%.
Push it down to -25% and let go -> it stays at -12%,
where in both cases it should return to 0% (exactly center)
This kind of deadzone issue is definitely the stick modules, and from china ordered sticks i've had deadzones as bad as +-30%. This is something you should test immediately upon receiving thumbstick modules - any slop at all in the modules should have you contacting the seller.
If that isn't the problem you're having, try describing your problem. I plug mine into my computer and use
https://html5gamepad.com/ to see exact numbers
