I have been tracking down the last few bug with the Saturn/SNES to Playstation converters. It turns out that some revisions of the PS2 and one PS2 to XBOX 360 converter both have messed up timing.
The acknowledge pulses come after the next data byte has started. Official controllers can cope with that, but some third party ones don’t work. I’m fairly sure it’s an error as Sony fixed it after a couple of minor revisions. I suppose the probably noticed that some third party controllers didn’t work on one port of the console.