I can't post supporting links to validate this, because they are not public message boards, however...
They just say what they need.
It's pretty pointless inviting diversity if you need to fill a village with "tribespeople" for an 18th Century nautical costume drama set in Fiji.
It's no good beating around the bush & asking for people with "brown skin" if they actually need people of Arabic descent or "white skin" if they specifically need Eastern Europeans.
Generalisations are OK if they really don't need a truly specific nationality, for example, they may ask for "people of South-East Asian descent" if they really don't need very very specific Chinese, Japanese, Korean etc. If they do, then that's what they'll ask for, or "people who are, or look like they are, of Chinese descent" etc.
They don't care where your ancestors came from, only that you fit the required description.
A friend of mine made a lot of money over the years playing Saddam H. who, of course, was of Arabic descent. My friend is Indian.
They will occasionally ask for "caucasian and a range of non-caucasian" people - I was recently on a shoot depicting race riots in the early 70s.
The lines for the plot were clear... 'whites' one side, everybody else on the other, so they needed about 50% 'white', 50% 'other'... which may not have been hugely 'fair' but is what filled the lens in a way they needed for the scene.
[btw, because of the subject matter, everybody made sure to be exceptionally nice to everybody else as soon as the call for "cut" was heard, as for the past 3 mins they'd all been hurling abuse & fists at each other. It was a heart-warming shoot; more hugs & high fives than I've ever seen on set :-)