Unlike the Apple TV and the iPad, and Amazon Fire TV and Tablet, or the Google Chromecast with Android phone, Xiaomi phones like the Mi Note Pro offer limited integration with Xiaomi's Mi Box.
However, you can do simple things like wirelessly mirroring the Xiaomi Mi Note Pro to the TV connected to the Mi Box using Miracast technology.
To set up wireless mirroring, first go to the Xiaomi phone's Settings->More->Wireless Display and turn on Wireless display.
On the Mi Box, on the home screen navigate to the far right until you see the green icon for wireless display. Select this icon to start the wireless display connection process.
After you turn on Wireless display, you'll see the Xiaomi Mi Box appear. Select it and you'll see the Xiaomi phone screen show up on the TV connected to the Mi box.
Hopefully in the future there will be more integration to control what you watch on the Mi Box from the Xiaomi Phones. For now, you'll have to settle for playing content on your phone and just mirroring it to the Mi Box.