The drums turn backward because they are on the pinion shaft, not the axle. So what is 'front' and what is 'rear' are reversed from what is on a pickup truck or car.
The stronger spring goes on the anchor post last and it hooks to the rear (I know they are angled; so let's say 'upper') shoe. You want the front/lower shoe with the weaker spring to contact the drum first and start dragging before the upper/rear shoe contacts the drum.
These are self energizing brakes, so, moving in forward rotation, the upper shoe will add its force to the rear shoe.
If the upper shoe contacts the drum first, it will slam the lower shoe into the drum, which I think is what you are experiencing.
You adjust the eccentric to hold the upper shoe up near the drum and the spring at the adjuster then can hold the lower shoe away from dragging on the drum.
If your springs are 'tired' you might want to get a maxi-kit with similar springs from NAPA. (If you can. Some NAPAs 'don't do tractors.') That's what I used to do back in the '90s.
That is the way I remember it at least. If I am wrong, someone else will correct us.