iTunes Movie rental oddity

Or maybe this is how it works?
I rented 2 movies from the iTunes store via my Mac Mini PC, which I usually watch on my TV via my Apple TV box. As I was going on a trip, I transferred these unwatched movies to my iPad Air. I didn't get the opportunity to watch them on the trip, so when I got back, I transferred them back to my Mac Mini.
Now they refuse to play through my Apple TV, but will play on the Mac Mini.
I know I read somewhere that you can transfer these movies back and forth and watch on any applicable device.
Any ideas?

From what I understand, the Apple TV can't have movies transferred to it like other iOS devices. It's strictly a streaming device, so it can't store a pre-downloaded pre-rented movie. You should be able to use AirPlay from your Mac mini to watch it on the Apple TV. More info in the link below:
Watching Rented Movies on Multiple Devices | iLounge Article