The first constitutions that were written by the American states after they declared independence were basically just expansions of ideas about government that had already existed for a long time in the colonies. They were ideas that had come out of such British innovations as the Magna Carta and English Bill of Rights.
Many of the colonists who came to America carried with them ideas that were relatively democratic. England was, at that time, the country that had gone farthest towards democracy. Parliament had strong powers that the crown could not take away. There were some rights that were protected by constitutional law. The state constitutions simply took these ideas a step or two further than they had previously been taken.
For example, the state constitutions did away with any appointed law-making bodies. Instead of having some lawmakers elected and others appointed, all legislative officials (and all chief executives) were to be elected by the people. In addition, state constitutions typically included bills of rights. These portions of the constitutions explicitly spelled out rights that were to be protected from the government. These were often very expansive, including such things as freedom from established religion, which the British had never had.
Thus, the first state constitutions were not revolutionary. Instead, they took British ideas that had come over with the colonists and expanded upon them.