No it does not. The parents would be here illegally which would exclude their children under Section 2 - Children of illegal occupiers of the US would not be.
Don't side step the point. Call them tourists. While they are in this country, the courts regard them as under our "jurisdiction." If consistency is applied, then people who are in other countries are under those countries jurisdiction.
We can't have one rule that applies at home, and an opposite rule that applies abroad. "Jurisdiction" needs to mean the same thing in all cases.