“Can you quote the legislation that required that?”
The Republicans passed the Reconstruction Act of 1867, which set the conditions the Southern states had to accept before they could be readmitted to the union, including ratification of the 14th Amendment.
Congress also declared that southern states needed to redraft their constitutions, ratify the Fourteenth Amendment, and provide suffrage to blacks in order to seek readmission into the Union. To further safeguard voting rights for former slaves, Republicans passed the Second Reconstruction Act, placing Union troops in charge of voter registration. Congress overrode two presidential vetoes from Johnson to pass the bills.
You are wrong on that. Here is a link to the texts of the Reconstruction Acts. You will note that in the first one it says that when a state completes all the acts required of it then "said State shall be declared entitled to representation in Congress, and senators and representatives shall be admitted therefrom on their taking the oath prescribed by law, and then and thereafter the preceding sections of this act shall be inoperative in said State." It does not refer to the former Confederate states as 'former states' or 'territories' but as 'rebel states'. It does not say that they are readmitted to the Union. It is clear that in the opinion of the federal government those states were never out of the Union to begin with. The idea that the former Confederate states were readmitted as states is a misnomer. They were not.