Apple tv and iTunes

I have 2 apple tv's in upsairs and downstairs. they are different generations. I have recently downloaded a tv series on the 2nd generation which is downstairs. it has been playing perfectly but does not appear in iTunes on my computer. It appears in purchased history in my account, but not anywhere else. I want to transfer the purchase to other apple tv.

Is it possible?

Or do I need to purchase on computer and then sync it to apple tv