I just found out that indexed shifters required mated cassettes, and I am using the rear wheel and cassette from an indexed setup with a non-indexed rear derailleur. I noticed backpedalling sometimes results in the upper pulley going askew as pictured, and always happens during an upshift. I never had this problem with my indexed setup.
I have two questions:
I understand simultaneously backpedalling and upshifting is bad, but does the chain falling off the pulley the expected outcome of doing that?
Is it okay to use a cassette from an indexed shifter from a 1990 shimano 105 with a non-indexed shifter like a 1996 suntour cyclone.
I've read the the very similar problem and I included a shot of the teeth of the upper pulley in case that might be the problem. Also, when the chain does go askew, I don't really feel the difference (I'm not a particularly distinguishing rider).