It's been many decades since I worked on an SA drum brake, so this is just a guess that might point you in the right direction.

One possibility is that the brakes are worn enough that the actuator cam is rotating up to top dead center. If so it'll not want to go back.

The other is that the shoes are a bit sloppy on the pivot, especially the one which the rotating drum would push forward away from the pivot. That could cause a self actuation as it rides higher on the cam. The tip-off is if it realease promptly after a full stop, or if you roll back a hair, but not when just slowing down.

I hope this helps, but as I said it's a shot in the dark.