These revolutions reflected the ideas of the Enlightenment because the Enlightenment was based on the idea of reason and rationality.
These revolutions were all based on the idea that traditional ways of deciding who had power and prestige were irrational. The French and American revolutions were opposed to the idea of power based on birth. Instead, they believed in the Enlightenment idea that all people (or at least all white men) were equal and should be able to participate in their own governance. The Haitian Revolution was based on the idea that one race did not have the right to enslave and rule the other race. This, too, was seen as an irrational idea. Thus, these revolutions were based on Enlightenment ideas that systems of government and privilege should be based on rational factors, not on things like birth and race.