First,let's look at three sentences:
1. My horse decided to run off with me on top of it. I do not know how i did not fall off .
2. Tightrope walking is a physical risk (e.g. you might fall off).
3. I fell down and hurt my knee.
In sentences 1 and 2, you are on top of something. When you are on top of something, you can fall off. You would fall off a roof, a sled, a cliff, a horse, a tightrope, etc.
In sentence 3, you are not on top of anything. So, you fell down. You could also just say ‘fell,.’ without ‘down,’ which I think is more usual:
• I fell and hurt my knee.