Your citation simply acknowledges that someone had been naturalized, and that as naturalized they now had the same status as those born into citizenship with the EXCEPTION of the presidency.
Congress decreed who HAD TO BE naturalized. The others who didn’t were born automatic citizens.
If you don’t need to be naturalized, then you are already natural.
Now, where is the definition of “natural born” in the Constitution?
Nope.
It's called the Right of Election. No one was told they HAD TO BE anything, nor was there anything 'automatic' about it.
2. Aliens by election are all such natural born, or naturalized subjects of the crown of Great-Britain, as were born, or naturalized before the fourth day of July, 1776, and have not since become actual citizens of the United States;
[snip]
Aliens by election may then be shortly described to be those subjects of the crown of Great-Britain on the fourth day of July, 1776, who have elected to remain such, and have not since become, and continued to be, citizens of the United States, or some one of them.
St. George Tucker, (Annotated) Blackstone's Commentaries
A person had to appear before a legal authority renouncing his/her former Allegiance and take a loyalty Oath to the United States...or some one of them.