Sen. Jacob Howard, author of the amendment, said:

This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the government of the United States, but will include every other class of persons.

….

It was not even the intent to include indians who existed at the time on the land:

Indians born within the limits of the United States, and who maintain their relations, are not, in the sense of this amendment, born subject to the jurisdiction of  the United States.

 

This underlies a broader concept of the Law of Nations that a citizen’s children are subject to the jurisdiction of the citizen’s country of citizenship.