From turbine engine investigation class:

Most engine fires are cowling fires. Once you pull the fuel, there's literally nothing to burn in the core. Stuff like hydraulic fluid, oil and fittings/material within the cowling will burn though. Some of these are composite materials too. Most engine fires below something like 20K feet are all "in cowling" fires. That's where the fire bottle goes, because there's no point in dumping it in the engine-as soon as fuel is cut, the light is out in the core. It's sending so much air in there that it smothers anything going on instantly. Above that ~20K altitude, the air is too thin to support combustion within the cowling, so you don't see the same kind of fires.