I asked Apple Support this question and they said to ask Premiere Pro people, because they didn't know.
When I export a 5.1 project from premiere in .mp4 or .mov, I can play 5.1 from my computer through my home theatre by way of Quicktime Video Player. But when I send those same files to my iPad and play them through the Photos app or through the Apple TV app, they only play in stereo. But the films I download from iTunes play in 5.1 through Apple TV from my iPad.
How do I get my videos to play in 5.1 through my iPad?
Very good question. Do you know what format and codec the films downloaded from iTunes are in? That might be a good question for Apple Support. I think the best place to start would be to look into what format and codec iTunes uses, and then we can see if that matches your export settings.
Also, are you using the same app to play the films downloaded from iTunes as you are to play the videos from your Premiere Pro project?