Oh brother. Your “source” also tells us that black people can not be citizens. Great job, there.
The past is a foreign country. The ideas they held then are not modern ideas, and many of them modern people will disagree with.
What they thought was common for their era, but you miss the point. Many of the people of that time period understood that English Law did not make "citizens", it made "subjects."
Alexander Smythe was not the only source from that era that regards Vattel as the source of "citizen."