So it seems to me that as long you’re running the app on iOS 10.3 or later it should call [SKStoreReviewController requestReview], and anything that happens after that is up to the OS.
I am not sure whether calling requestReview() in the Expo app vs. a standalone app makes a difference, but I could understand if it did, because any reviews would presumably be for the Expo app itself and not your “experience” running on the Expo app.