Apple TV 4th generation (version 9.1)
iPhone 6 s (iOS 9.2)
It wasn´t fixed with the update.
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Last Saturday (2015/12/5) I called Apple TV´s support. After explaining the issue to the operator he put me trough to a technician. Once he reproduced the issue, he called me back and told me that this is an iOS´s issue that has been on board since iOS 8.
He said he was going to check out with the development team to see whether they are going to fix this bug or not (and leave it as «spec») and will contact me this week. I´m still waiting and I´ll post any update here.
They gave me the impression that they were not aware of this issue.
I live abroad and being able to Facetime my family with a big screen was one of the main reasons of purchasing this Apple TV. Before buying it, I went to an App Store to check if Facetime is working properly, we made a Facetime call test on an iMac and it worked, though we didn´t try the landscape mode (I took it for granted that it´ll work). How wrong was I!