Movie icon shows up on Apple TV with airplay but movie still plays on iPad

I rented a movie tonight on my iPAD (first generation, running iOS 5.1.1) and tried to use airplay to watch it via Apple TV. The Airplay icon appears just fine and I can select Apple TV. When I do that, on the TV, a small icon of the movie (just the movie poster) appears in the lower right hand corner, superimposed over the main Apple TV selection screen. If we moved the cursor on Apple TV to "Computers", the movie icon appeared larger, in the upper right hand corner. If we selected that, it went to a screen with just the movie poster and the time bar at the bottom. The movie was playing on the iPAD but the time bar was running (with the movie poster) on the Apple TV. It almost looked like the Apple TV was streaming to the iPAD instead of the reverse...

We reset, restarted, restored the Apple TV. We rebooted the iPAD twice. We reset the router as well. The Apple TV is a second or third generation (bought it in fall of 2012).

Is the issue that my iPAD (and iOS) is just too old to work with the newer generation Apple TV (if that's the case, why did it appear to connect in such a weird way and just not play the movie)

Is something wrong with the Apple TV?

So frustrating. This stuff drives me nuts.