When Turbo.264 is connected to your Mac, you can use the Turbo.264 software to export to Apple TV. 

When Turbo.264 is connected to your Mac, it will also speed up your AppleTV exports from EyeTV. Connect Turbo.264 to your Mac via a USB port, then launch EyeTV 2.4 or higher.

In the Recordings section of EyeTV, select the recording you wish to export to AppleTV. Go to File menu, select Export and choose AppleTV.

After a recording is complete, select your recording and click the AppleTV button.  When Turbo.264 is in use, you’ll see the red progress bar, and there will be a series of pulsing circles below the export bar.

You can automate the exporting process by specifying AppleTV when you schedule a recording. Go to Schedules, select a scheduled recording and click Edit Schedule.