While jabbing i step on the front foot but only a little 5-10cm then the left shoulder turns in as the lead arm is pushed out (eyes look straight down the arm), The lead arm should only twist at the very end making it harder, then the arm is pulled back at the same time the shouder is also pulled back.

As this is all happening the legs are moving also.
The front leg after the small step is straightening, pivoting and pushing back (Your ass should move away from where you are punching) and the rear leg pushes forward.
This gives you more reach and pushes you away from any body counter.

This is all from a squated wide stance with the rear leg bent. up on your rear toe with the foot facing forward.
You should be relaxed as stated, with only the hand tensing before impact.
A fast jab will bring a shock factor to the opponent as they wont see it coming as easily as a hard jab with a tensed arm that appears to come from 2 streets away.

I am quiet tall with a long reach over 2m. And this is how i get the most out of my reach. The jab is very important to my game and im always working on it. I probably throw 4-5 or more jabs:1 of other punches. And i work it like that on the bag also.

Wytster: As your shadow boxing you could try get a squash ball and put a small cut in in 2-3mm then put it in your hand(I use middle and ring finger to hold it). As you punch just hold the ball and as your about to hit your imaginary target (full extension) squeeze the ball/clench your fist it should make a hiss. Then relax the hand again and pull it back. This should help you to relax the muscles in the arm whilst punching.