So if I have chain on the 53 in the front and 25 in the back and turn the crank backwards, the chain's not supposed to skip off, is it?

The gears seem to shift well enough and all that, but when I have the bike in a stand and put it in big/big and turn the crank backwards, the chain eventually upshifts itself before completely falling down the cassette. The crank and chain were newly installed, and I don't think I was having this problem before with my old setup. Could it be a derailleur position/tension adjustment? Stiff links? Chain too short?

Thanks.