Unfortunately the word (free) ‘Persons’ is used in place of ‘citizens’. It’s basically a head count irrespective of citizenship status. An serious oversight on the part of the drafters IMO.
Well they weren't perfect and couldn't foretell every challenge (Sorry Ron Paul supporters). Fortunately they left us with an amendment process which although difficult is probably the only way to legally deal with this issue... along with enforcing the law so illegals aren't here for the head count in the first place.