Not automatically a US citizen?
You (and this applied to me also, US Born Citizen of US Citizens) that in order to be able to pass on US Citizenship to your children, you must have lived in the USA for 5 years, 2 of which have to over the age of 14. Hence I have to wait for the daughter to turn 16 here in the USA.
The daughter was born in Thailand, and I had to meet that requirement at the US Embassy to get her US Citizenship. Even had to do a DNA test to prove I was the biological father.