Full paid T-mobile iphone6s doesn't work with ATT network

I pre-ordered an iPhone 6s (A1688 T-mobile version, full paid) and i got it today. I'm using ATT as my carrier, but I heard that all full paid version is unlocked, so I brought an T-mobile version for convenience(no information required during order process). The T-mobile version phones(A1688) supports most of band that ATT version(A1633) has, except LTE band 30.

After putting my ATT sim card into my new iPhone, the calling or messaging works fine, so it should be true that full paid phones are unlocked. But cellular data doesn't work. It shows 4G on top left of phone, but actually disconnected form internet. Also, the APN setting menu can not be found in the Settings, so I'm not able to change APN setting. After imported the profile of ATT network from unlockit.co.nz(changed APN setting this way), finally I can access internet with 4G. LTE doesn't work there, but I can access LTE network using my friend's iPhone 6, so the problem is on the phone not the coverage of LTE network or my ATT account.

It is OK just not having LTE, 4G is enough for me, but Personal Hotspot is not working either. I really need this. In the cellular settings, it says setup your personal hotspot by contacting your carrier. But I can use Personal Hotspot on my old iPhone, so the problem is still on the phone not my account. If this problem can not be solved, I have to return it to apple store and buy an ATT version. I'm a student and the nearest apple store is somehow far away form my home.

If there's someone like me who want to buy T-mobile iPhone using other carriers, be warn of this.

Could any one give me some advice for this?