So Qimage embeds the printer paper profile into a jpg or tiff file?
No, it does not when printing.
'Embed icc profiles in saved/converted images (jpg and tiff)'
This means when you convert an image, and you specify to convert to a different space, the profile is embedded in the image - you would not normally use a printer profile although there are some circumstances when you might do it, like when sending images to a printing service and you embed their profile.
It sounds as though there are some missing parts to your account of what was happening, just ticking that box would not have made a difference to anything printed with Qimage. It could for anything converted in Qimage and printed in PS, But PS warns you about embedded profiles and anomalies.
In your "messing about", something else was changed, probably related to colour management settings or the way the image was converted. It may be a good idea to try to discover what else you changed, so the same error is not made again
Terry.