It's certainly unusual, but what may be causing that would be if portrait orientation was locked, and / or mirroring was turned on.
If you swipe up from the bottom of your screen, you can manipulate the mirroring options (where the TV shows app output vs. just a mirrored image of what's on the screen).
This control center is also where you can check your portrait orientation lock settings with the icon at the top of the screen - it's typically an arrow forming a circle, but if there's a lock in the center of it, your screen orientation is locked.
If you're still encountering trouble, perhaps hard-rebooting the device will help. You can go to your home screen and try the steps from this article to see if they make a difference.
Playing with the settings I mentioned above may get you some results but if not, there may be something in the TV or projector settings that could be contributing to the dilemma. Our expertise is unfortunately limited here, with the various models of TV / projectors and their settings falling outside of our knowledge range, but we're happy to keep helping in any way we can.
If there is anything else we can do for you, please feel free to submit a support ticket and let us know!