Hmm
Thats really kind of weird. I wonder why T-Mobile's having problems with iOS 10 and we're not.
Our network is also in the US and GSM/LTE (which kind of narrows down who I work for as there are precisely two), but aside from the usual, routine Apple problems like IMEI mismatches, its been fairly smooth with iOS 10. I'd say it is indeed their carrier software, though ours being better than theirs doesn't happen that often. Hell, this might very well be the first time thats ever happened.
I did have someone fuck up their phone the day it came out, but it was more because they're a moron than anything the update itself did.