In the original tweet the aide is referred to as 'Lady' somethingorother so presumably titled aristocracy. I expect that the very very posh have a good idea of exactly where they're 'from' as they need to have traced their ancestry for the purposes of titles and inheritance. Just look at the mention of Richard Grosvenor Plunkett-Ernle-Erle-Drax and reparations on this forum, he's got all those names and can trace his ancestry all the way back to wheneveritis because of the need to preserve the dynasty. It's also (very obviously) tied to notions of empire and colonialism etc so we shouldn't be at all surprised that an extremely posh person should ask this type of question of a black woman. She may well be used to hosting foreign / Commonwealth dignitaries and subjects who may have different attitudes concerning where they are 'from', rather than charity workers from Hackney.
It's certainly interesting in terms of race, class, citizenship, empire and people's notions of their identity and position with our society and its heirarchical structures.
Edit: Although Sistah Space say they have no intention of naming the aide involved, she has been identified and as well as being posh as fark, is also 83 years old. Which might have something to do with it and one might hope that younger palace employees have a slightly more modern attitude. OTOH, it's the Royal Family, what do you expect? It's built in.