Yes, they are. "Not subject to the jurisdiction" means outside or above our laws, as in the representatives of foreign governments. Our laws do not apply to them.
It doesn't mean "people that we haven't caught yet." That's twisting the language to make it say what you want it to say.
They are held accountable by other documents, not the Constitution. They are subject to whatever jurisdiction we deport them to.
Even if one wants to read it -regardless of authors stated intent- to mean the newborn "person" is now a "citizen". In no way would this apply to the parents.
I suppose we could give them the option of leaving with the "citizen" or without.