The adjuster lever is the only thing touching the star wheel. It should be touching 100% of the time. It should be parallel to the star wheel.
If not then the length of the cable could be wrong, or the routing of the cable.
There is a spring that returns the adjusting lever all the way down and tightens the cable when brakes are released. It there a spring present to return the lever down?
Do you have the lever that mounts on a pivot pin through the shoe? Or do you have the lever that just clips in a hole in the shoe?
Mick, look at the FSM picture posted and compare. Show us a picture when you can.