I can't tell you exactly what sets off the auto feather device, I believe its usually when an engine fails (dies), the prop will rotated to create less drag and will not "windmill"

feather angle reduces the yaw effect of a still prop.

i think autofeather puts the prop in feather when the shaft tourque goes under a certain limit.

Starting from the prop site, moving to the engine
Spinner
blade pitch controls, autofeather mechanics are in here
Clutch to make starting easier, prop is spinning free until RPM above a certain value
Reduction gearbox
Rest of engine