He did write citizens. Persons become citizens provided the are
a.born/naturalized
and
b. subject to the jurisdiction.
Illegal aliens and their offspring, although held accountable for their actions while here, are not subject to the jurisdiction.
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.