When you are on your PS4, launch the video streaming service that you would like to view through your Vita or PlayStation TV. After app has launched on PS4, press PS button on controller and go to the power menu. Select “Rest Mode”. After letting the system go to rest mode, use the PS TV or Vita to boot up the PS4 with Remote Play. Once remote play has started, go directly to that video app and you should be able to use it just like you would on the PS4. Source