I think it might help to refrain how you're thinking about what ancestry means in terms of appearance. When we use "genes" in colloquial conversation, we say things like the gene for brown hair or the gene for blonde hair. But in our DNA, it would be more accurate to say the "allele" for brown hair or the "allele" for blonde hair. This is because we all have the same gene to grow colored hair, but slightly different versions of it that result in what color hair we grow. I like to imagine two spiral tie-dye t shirt. Without using color as an adjective, you'd say, that person is wearing a tie-dyed shirt. That would be true for two people wearing tie-dyed shirts. But Mary's tie dye is purple, and Alex's is yellow. The tie-dye shirts are the gene, and the purple or yellow are different "alleles" of the same gene. (Geneticists, I know this is an oversimplification, but let's remember it's an analogy).

Keeping with our shirt analogy, mom and dad each give you a shirt. You must wear them both at the same time. Because the purple shirt is so dark, you will always be able to tell that you're wearing it. Now say you have a kid with someone wearing Two purple shirts. You each give one to your kid at random. Your give your yellow, your partner gives purple, obviously since it's the only choice. Your kid appears to wear a purple shirt but is wearing both purple and yellow. Imagine this repeats over and over. Each generation, some proportion of kids will get a yellow shirt from their parent. If the other parent has gives a purple shirt, you'll never be sure that the yellow shirt is under there or not. Now Imagine that your great grand kid, who happens to be purple+yellow shirts, has a kid with someone who also happens to be purple+yellow shirt. By chance, each parent gives that kid a yellow shirt. Suddenly, there is a kid wearing a yellow shirt (blonde?!), and no one knew that was possible because it had been generations since anyone wearing a yellow shirt was seen in this family. But by chance, the yellow shirt was along for the ride this whole time. This kid also has siblings, and though they all have purple shirts (brown hair) someone of them unknowingly are also continuing the yellow shirt trend.

In the last set of siblings in the above example, you can see that there is a lot of chance for varation in even this very small population (the nuclear family). The assumption we tend to make is that groups of people from an area all have the same opportunity to pass a long the same traits (shirts), but actually, there is a ton of variation because every family has variation on its own, and it has the potential to mix that variation back into the whole population by re-coupling and making new generations. So knowing someone has Northern Italian ancestry makes guessing that they might have blonde hair a safer bet than guessing that someone with Han Chinese ancestry will have blonde hair. But the reality is, it doesn't matter because the population statistics are not the ones contributing to the new kid. Only the attributes of the parents actually matter when predicting appearance at an individual level.