If “jurisdictions” meant merely being present on our soil and then obeying our laws (excluding, apparently, illegally arriving here), then there would be no need for that word “jurisdictions”.
It would be simpler and MORE EFFECTIVE to simply say “anyone born here is a citizen” if that is what they meant.
But they clearly did NOT mean that.
Yes there would. Diplomats and invading armies. That's the extent of application of "subject to the jurisdiction", as popularly applied by courts for the last 100 or so years.