How photoshop deals with RGB numbers is customizable in color settings. The normal (and most sensible) setting is to preserve the embedded profile. This means that the embedded profile becomes the working space when you open the image. All the numbers you see in the photoshop color picker will be in relation to that space. So your ProPhoto TIF in your original question is brought in with RGB numbers unchanged and transformed in accordance with the file's embedded profile. No conversion to another space happens unless you explicitly ask for it (or have set you color settings to convert to the default space when opening images).
Mark, I'm beginning to get it, I think. The confusion for me is that my version of Elements has limited stated color management. Anything other than sRBG and aRGB is not mentioned, but it will open a ProPhoto image without complaint and will actually save it thus profiled after editing. Classic Adobe . . . I'll bet it would take Adobe Wide if I tried.
I didn't fully get "RGB numbers unchanged and
transformed" though. Does it mean that the numbers are transformed to a space, say ProPhoto, as part of the RAW conversion and then brought unchanged after the transformation into the, e.g. Melissa, working area along with the profile or knowledge thereof? Thus, our RAW yellow would be transformed into a D65 ProPhoto file as 234, 251, 84 and the profile says to the monitor profile "this is 100% saturated yellow in your space" which shows on the perfect screen as D65 sRGB 255, 255, 0.
RAW files and Lightroom are a little different because RAW files aren't really in an RGB space until they have been converted from their RAW format. Lightroom handles this by converting the RAW internally to a space almost the same as ProPhoto RGB (Melissa RGB). The numbers you see in Lightroom are the RGB numbers in that space. When you export from Lightroom to a TIF or jpeg, only then does it get converted to a regular RGB space like sRGB, Adobe1998, etc.
Not sure if that answered the question…
Yes, it does indeed. Especially the mention of 'Melissa' RGB. Not for Adobe the de facto
ROMM standard, aka ProPhoto, gotta luv 'em . . . can't fault their business model, though!
I'm off to play with 3 different converters and see how they come with sRGB numbers for a reference pixel in my sunflower image. Well it's after dark and I'm retired so that would be fun in my world.