After the latest iOS 11 update I experienced a problem with HomeKit remote access via the Apple TV. I was wasn’t able to get access to my devices outside the local wifi i.e. LTE/mobile network.
The solution was simple: update also to the latest tvOS, then goto Settings, Account, iCloud, HomeKit. Click on the option so that it displays „Disconnected“.
Open the HomeKit settings in iOS on your phone in the HomeKit app (in the upper left corner), under „Control Centre“. If you see „Standby“ then wait for „Disconnected“ or „Not connected“.
Activate HomeKit on your Apple TV again and wait for the HomeKit setting to display „Connected“ again.
You should able to access your devices in the HomeKit app again or at least see their status.