This is a tough one. We know:
The bird is VERY RARE.
The man sees SOMETHING HAPPEN TO THE BIRD and is scared.
Whatever happened to the rare bird happened while it was IN FLIGHT.
A FEW MINUTES PASS before the man starts screaming.
The man is afraid for both his OWN life and the lives of OTHERS.
The man was going from AMERICA to AFRICA.
Maybe the man was on a plane over the ocean when an endangered species of bird was sucked into the engine. At first there is only a little bit of smoke then after a few minutes the engine explodes into flames and the plane goes crashing into the sea.