The Canal Zone was a US Territory at the time too.
Tuaua FAQ - We the People Project
I start there just because the legal stuff is dense.
And on the subject in general (not relevant under US law, but interesting from an international perspective, which is what happens when citizens of country have babies in another country) ...
Displaced in the D.R., by Rachel Nolan | Harper's Magazine | May 2015
How the Dominican Republic reversed "anchor baby" in their country.