On Apple TV the app shows a record button while watching live TV when swiping down via Apple TV remote app.
However, when using the app on an iPhone or iPad while watching live TV (on the said device its self) when taping the screen to show info, seek, etc.. there is a lack of a record button/option.
The only way to record on iPhone / iPad is in the prompt what to do when selecting a live program in the guide. Unfortunately when backing out to return to the prompt menu to record the program then the watch buffer is gone when you leave live TV and is not apart of the recording when you begin recording from said menu prompt. Hence why the record button is expected while watching live TV.