From my experience, the most common way for smoke to get to a detector in the living area from a fire developing in the attic is to compromise the AC duct system, particularly the plastic version reinforced with wire, and allow the smoke to come down through the ceiling vent. How long it would then take for it to activate depends on several factors: where the detector is located from the vent,how many exposed ceiling joists the smoke has to cross to get to the dectector,how close the detector is from the peak of the ceiling,and whether the detector is mounted on the bottom of a rafter or on the bottom of the ceiling.

In this scenerio, by the time the detector activates in the living area, the attic and roof are generally well involved, with the fire venting upward and creating minimal impediment for the occupants to escape.

However, if for some reason the fire had burned long enough in the attic to allow rafters or other roof structures to fail and fall through the insulation and ceiling covering before smoke could get to the detector,this would accelerate the downward spread of the fire and if the living room was the route of escape, this could be a problem as the alarm would be now be alerting to fire in the living room insted of the attic.