Down and back are not used together in this way.
He fell down backwards (don't forget the s) is fine.
He fell back is fine.
He fell down is fine.
But for some reason not fell down back, in this context anyway, as the two directions seem to contradict each other. He fell down backwards means he fell and landed on his back. He fell back also means he moved backwards but doesn't necessarily mean he hit the floor. He fell down means he landed on the floor and it could have been in any direction/position.
He fell back down would mean that he had already been 'down', moved up, then returned to 'down'. For example 'He struggled to free himself from the mud but fell back down. You can find some ways to use 'fell down back' in this sense, with back meaning to return to rather than the man's physical back. For example 'He struggled to free himself from the mud but fell down, back into the ditch.
Hope this makes sense!