Honestly I think I would advise against rotating the eyes. Besides it not being at all what makes people look asian (any photograph of an asian person will in fact have rounded eyes that sit normally), it's also been used as a rather lazy/ offensive stereotype in the past.
These are some things I've noted tht add up to a common look when I studied photos of people from various Asiatic backrounds. Epicanthic fold is the most common for eyes, but some Asian people don't have, just as some Caucasian and African people do in fact have it.
Facial structure is usually very rounded and rather flat, so I wouldn't have the cheeks protrude nearly as much. A trick I use is to have most of the line weight concentrated at the "back" of the eye, where the fold reveals the eye more fully. Around the front the skin appears tight, so the line weight is left much thinner. Eyebrows are interesting, they're commonly very short in length and start thin, and thicken out at the end, for both men and women. I usually avoid drawing much of the bridge of the nose from front on as well, because it projects less and slopes quite a bit in side profile (that's just my personal style though, eliminate detail that isn't very prominent.)
Honestly what you had wasn't too far off from looking Asian. If anything I think the other kids could have more experiments with different eye shapes.