An engine flame out = negative torque, prop windmills and tries to turn the engine = large drag.
The hydraulic NTS system lets prop move to an increased blade angle = less drag.
Negative torque ceases when windmilling engine drives prop again = NTS operation stops.
NTS system will not fully feather the prop it must be done by the PILOT if unable or doesn't want to relight the engine.
Feathering: "NTS/auto feather system gives prop feather operation together with an engine shutdown but only available when APR is armed" (which it always is as per SOP's and check list item)