I totally agree with the things people are saying here. We don't always know the exact place a person or their ancestors came from, but we do have words for describing people. Black, African, Asian, Middle Eastern and so on. I think it's best to use them when needed. Of course, there are differences in how different English-speaking countries describe these terms.
I understand that the UK version of Harry Potter relied more on things like Lee's dreadlocks and Cho's name to designate their ethnicity than the US version did. Still, Rowling didn't mention that Ron was white (of course, having blond or red hair tends to make people assume "white European," even though red and blond hair do exist in other parts of the world).
I write fantasy set in a secondary world, though, one that has no Asia, or Africa, or India. And some of my characters are people who resemble people from these places. Coming up with descriptions that aren't overtly racist, and also inaccurate (like "almond-shaped eyes") has taken some thought. Coming up with short (I don't tend to dwell on the minutiae of any character's facial features anyway), clear, and non-racist descriptions of facial features is defeating my skills. Because, in fact, there really isn't any one trait that defines all people from a region. People are incredibly variable wherever you go.
So I do worry that some readers will think these characters are simply white people with dark hair and a tan. One thing I do is mention the skin tone of my white characters too at some point. Olive, pale, ruddy and so on.
I try to work in (via their own pov, or the pov of the person meeting them for the first time) that they presumably have ancestry in other regions of my world from the current setting. "She had the dark brown skin and tightly-curled hair that was common in northern [insert continent name]," or "he had the amber skin, soft features, and dark hair possessed by some people from southern [insert name]."
The theme of being an outsider in my society pervades the story (every character, white or Poc, straight or LGBT, male or female etc) is an outsider in some way.
But I can't help wondering if some people won't still see the PoC characters as white. Does it matter? Probably not in terms of the plot. But as an aspect of world building, I think it does. I want readers to get a sense that there's a larger world out there, one where migration, trade and cultural exchange between different people has been going on for a while, and this has created both enrichment and friction. Some of this enrichment and friction is relevant to the plot.
And maybe it matters to some people who are just tired of everyone always defaulting to white in the majority of secondary world fantasy novels. I'm of European descent and am fascinated with European history, but even so, I was getting pretty bored with fantasy that attempted to recreate a "medieval" Europe that never was, one where everyone was white and there were no real cultural differences between people (or if they existed, they were provided by stock in trade fantasy races, like elves and so on).
Is that PC? Maybe. But for me it comes down to my writing what I'd like to read. I hope I haven't screwed up, but if I have, I'll try to learn from it.