"it further provides for the children of aliens, whether born within or out of the United States."
Aliens - whether born within or out of the United States.
Aliens born within the United States.
I hate to pick a nit because you make a very good point here, but the sentence you quote can be read in such a way as to say nothing of the citizenship status of the children of Aliens.
The term "Aliens" is applied to the parents. It is not specifically applied to the children. Taking the Devil's advocacy in this, I would assert the children could still be "citizens" though they remain the children of "aliens."
The status of the children as either citizens or aliens is not clarified.
Perhaps it is clarified in the larger context?
The Report appears in the Congressional Globe of the 28th Congress, beginning on page 129.
The Naturalization Act of 1802 (2 Stat. 153)