Excellent.
According to the amendment, if an alien has not yet been naturalized in the US, then they are not subject to the jurisdiction of the US. The writers obviously are not talking about having to follow the laws while they are here.
I can think of no example of a naturalized citizen who is not subject to the jurisdiction of the US.
Illegal aliens have deliberately avoided being subject to the jurisdiction of the United States. Hence their children would not be natural born citizens or citizens under the 14th amendment.