Don’t know about ethnic Chinese turning to the right. If you look at parts of the San Gabriel Valley and Orange County where there is a large ethnic Chinese population these areas have or are becoming Democratic areas.
In my experience, Asian immigrants — even many wealthy ones — tend to be docile peasants with a herd-like mentality. That makes them a natural Democrat constituency. But they also despise welfare in all forms, so the GOP can certainly make some inroads among them.