Apple TV Remote option in iPhone Control Center doesn't work
My guess is that you’re using either a 2nd or 3rd generation Apple TV. 

The iTunes Remote and Apple TV Remote apps available from the iOS App Store will work with all Apple TV units going back to the Apple TV 2. However, the Apple TV Remote option you can configure as a control in Control Centre will currently only work with the Apple TV 4 and Apple TV 4K units. Unfortunately, Apple hasn’t made this obvious in the user interface and as a result no error or info message is shown to let the user know.