Two Caucasians (ethnicity) who are US citizens living in China gives birth to a baby in China, then the baby would be Caucasian (ethnicity), and American (nationality, by US law), but probably also Chinese (nationality, by Chinese law[1]).
Maybe that example is not so great because the baby would have dual-citizenship, so consider a different example:
3rd generation Chinese immigrants in the US who are born in America, never left the US to visit China (same as their parents), it is their grand parents who migrated from China. These 3rd generation immigrations are Chinese (ethnicity) and US citizens (nationality), also called Chinese-Americans (format: [ethnicity]-[nationality])[2]. These Chinese-Americans are not citizens of China, but they are ethnic Chinese.
Hope that clears up that one small point.
[1] Most countries have a 'if you're born here, you get our citizenship automatically' (I'm not sure about China specifically, just using it as an example).
[2] easy to mix up and confuse, but order matters here
That principle is called 'jus soli'[1], and is far from universal. Only ~15% of all nations confer it. A few more grant it under restricted conditions. China is emphatically _not_ one of those countries.
The term Caucasian is highly confusing as it's a racist term invented by the same German who came up with Negroid and Mongloid, and is - as far as I know - only used in the United States. In fact, the Supreme Court in United States v. Bhagat Singh Thind (1923) decided that Indians were "Caucasian", but were not white.
Also, China is a bad example, as Chinese is not an ethnicity, it's a nationality as China is a multi-ethnic nation. The ethnicities being Han (what most people consider to be "ethnic Chinese", Hui, et al.
So presumably Tesla was a Croatian-Serb, or possibly a Serb-Croatian, and whether or not those two groups get along doesn't really affect that definition. I mean, I fully understand that it is a touchy subject, but I don't really think that it affects long dead physicists very much.
It's still American.
(At least to us Europeans) what matters is the culture of the parents/kid, not the nationality or the ethnicity itself.
A 3rd generation Irish-American is an American, not an Irish, and a 3rd generation Chinese-American is by all means an American too.