As for the plane, the rate of descent at 450 feet was 30fps not 500fps: ...the plane was just 450ft (150m) above the ground.... A second later, the plane reached its lowest flight altitude of 450ft and a second after that the ground warning system barked: 'Terrain, Terrain. Pull up, pull up!'
Earlier it had been 500fps before the autopilot kicked out.
Too much "unexpected tail wind" will bring you down quick, which is why the controller wanted them to use runway 06 (East into the wind approach) instead of the pilots requested (and approved) Runway 24 (West downind). The winds in the mountains vary quickly.