In the citation the article gives, we find:
Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other PersonsNote that they give an exception to "free Persons" -- "excluding Indians not taxed". Indians not taxed were not "citizens". But they felt they had to exclude them, which means that without the exclusion, the term "free Persons" would have included Indians.
Then they say "3/5th of all other Persons". This is slaves -- which means slaves were considered "Persons". Slaves were clearly not citizens, and most were not born here, so they were immigrants.
Persons therefore cannot have a "special meaning" in the constitution of "citizens".
The 14th amendment doesn't change that:
counting the whole number of persons in each State, excluding Indians not taxedAll they did was remove the "3/5ths" part. They didn't change what "persons" meant, or suggest that persons had to be citizens.
In fact, the entire 3/5ths compromise proves the article wrong. Why did we need a "compromise"? Why not just ignore slaves? The south wanted them counted for apportionment, so they got them "partly counted".
Having done quite a bit of genealogy using census, they did indeed count non-citizens. In some years, they asked if the person was naturalized, year of naturalization, and country of origin. But I’m thinking in those days they were mostly legal immigrants.