I've always thought of it via the example of an explorer as the first stranger on an isolated island. All births before had been natural born because there was no other possibility. All births had been children of natives. If the explorer impregnates a native and a child is born, tribal elders would have to convene to determine the child's citizenship, that is, they now need a some kind of law or rule. If they decided the child was an islander, the child would have been naturalized, IOW converted from a non-native into a native condition.
Natural born means there's nothing else they could be; not natural born means some ruling is necessary to determine citizenship.
That's my take from Vattel's passage wrt to births to natives. As you say, it's not a law Vattel was describing, rather an application of common sense.