I just found out that if you use the same email address as Amazon accounts in different countries, you must use different passwords respectively. Otherwise it will go to your US account or maybe arbitrary on the Kindle app of your mobile devices. It doesn't have problem on PC web because you are able to specify the URL like amazon.cn.
Originally I guessed the Kindle app would check where you were from the mobile device region or the app store region where you downloaded it.
Interesting strategy for this kind of things. Clever and Flexible.
Now I can read English books on my Paper White and use iPad for Chinese books from the CN store.