“Isn’t ‘at birth’ when you said it happened? Congress says it is.”
Naturalization is the process of becoming a citizen through a process specified by law. It CAN be based on when and where someone was born, but it does not make applicable people retroactively citizens at birth. So, for example, Congress amended the Constitution to insure that blacks who resided in the US were unquestionably citizens. They did not have to apply to become citizens, but they were naturalized.
CHAPTER IX. Of the Enumerated Powers of Congress
I hope those help you better understand what that phrase means.