The most common reason people get diarrhea after eating scrambled eggs is because of an intolerance to eggs.
Eating the scrambled eggs the eggs trigger an intolerance if your digestive system has a difficult time processing a certain aspect of the egg.
That can then lead to diarrhea, bloating, stomach aches etc.
Having an intolerance to eggs including scrambled eggs is not a life threatening condition but it can make you feel awful.
The eggs could also be contaminated with bacteria which could be causing the diarrhea but if you cooked the scrambled eggs all the way through and they are not runny etc then they should be safe to eat as cooking the eggs properly kills the bacteria.