Now, would an illegal Mexican living in the US who then goes to Germany have a requirement to file US tax reports?
Congress has the wide latitude as the US Constitutional body to make uniform rules of naturalization, and this also includes implementation of laws under the 14th Amendment.
Many of the same Congressmen that brought about the 14th Amendment 6 years earlier clarified citizenship as seen here in the New York Times on March 30, 1874. They understood the intent and meaning of the Amendment.
On income earned in the US, yes.