I think this is what’s happening.
When you open the tif with profile embedded, RT sees it and all is ok.
When you open the other one i.e. no profile, with “Use embedded if possible”, then of course RT doesn’t know it’s adobeRGB, so I reckon it assumes sRGB. I think this is confirmed because I opened the no-profile one in Gimp, assigned sRGB, output to jpeg, and it was the same image as the RT one, by flicking between the files using the built in Ubuntu viewer “Image Viewer”, which I believe obeys profiles, so no risk of RT monitor profile issues muddying the waters, because not using RT (or Gimp) to make the comparison.