Answer:
Ill try to explain this as best I can
They didn't have freedom. when they fought the war and won their world turned upside down because of the freedom they earned. They never thought they would see the day they won their freedom, but they did. So, the day they won the war, "the world turned upside down". That is why the "world turned upside down" is a fitting tune for that scene of the Alexander Hamilton play.
hope this helps!!!