I think I have a simple answer to your question. If you look at the examples I think you will have your answer.

1. When the Colonies United as the United States and won their Independence the people either accepted citizenship under the new government or left back to their desired citizenship under the Royal Crown.

2. When the French territories were bought by the United States the citizens either accepted automatic citizenship under the United States or left back to the citizenship of the French Government.

3. When the Spanish sold Florida the citizens of Spain rolled over as citizens of the United States under treaty agreements. All freed men stayed free, this was good for freed blacks, and were allowed to be citizens of the United States or go back to Spanish ruled territories.

4. When a U.S. territory becomes a State, the people within that territory become Citizens of the new State.

In other words its automatic unless there is a treaty involved and then those agreements take over.