I use the Mad Catz C.T.R.L.i and have no problem with it, it's a decent pad. Although I am thinking I might buy a Nimbus as well, I like the look of it.
As for Crossy Road, it does work, if a little temperamental at times.
For me the steps to get it working reliably are. Quit both apps completely from the task switcher and start them up again. On the games main screen on Apple TV, swipe up from the bottom to open the character picker and scroll along to the two player game on the left.
Click to get it started on the Apple TV and click to make Player 1 ready.
Then on the iPhone tap the button on the bottom right of the screen and choose the GamePad icon at the top of the list.
At this point it sometimes takes a second or two to connect.
Once it does, tap the play button on the iPhone and that's it, the games ready to start.
I guess that's what everyone will be doing, but I figured I'd just do a wee write up as some people have been having trouble with it. Only other thing of course is to make sure both Apple TV and iPhone are on the same WiFi Network if you have more than one enabled.
Oh, while we're on the subject of controllers. There's a good website
here that keeps up to date with all of the MFI Game Pads, does reviews, has compatible game lists and so on. It's well worth a look.