Thanks for all your help and investigations. Much appreciated.
I did some additional testing too, and it turns out that if I copy a password from SafeInCloud it doesn't get stored in the clipboard history (so that option in Alfred seems to work as expected). But as soon as I paste it in Firefox it does. This behaviour disappears though if I disable the SafeInCloud Firefox add-on/extension.
So even if I don't use the Firefox extension but simply copy and paste, it still has an impact on the clipboard history. Perhaps that's in line with your findings. I'm not too familiar with the details of the AutoGeneratedType flag and how/where it kicks in.