The author should have made sure that wording was in the amendment...
The author was not the only cook in the kitchen.
There was no concern at the time. Amendments are not written to cover every imaginable concern. That is why SCOTUS reviews intent and meaning by inspecting the Congressional Record.
Lets assume the drafters of that amendment were not morons. They had a choice between:
1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside,
and
2. All persons born or naturalized in the United States are citizens of the United States and of the State wherein they reside.
They chose and ratified the second version. The only logical interpretation is that the phrase and subject to the jurisdiction thereof was intended to have a restrictive meaning. President Trump is correct - the author did make sure that wording was in the Amendment.