Ah, now I’m not specifically familiar with RT’s logic, but here’s what generically is probably happening:
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As you work on your image, that work is applied to an internal copy that conforms to the working profile. What you see on the screen is (or should be) converted from that profile to the display profile.
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When you save to, say, a TIFF, that “Output Profile” setting is used to convert the working image from the working profile to the output profile, and that output profile is then embedded in the file to follow the image that conforms to it.
Now, if you regard the histogram of your image prior to saving it, I think in RT you’re looking at a histogram of the internal working image. If you then save the image to TIFF with a different output profile, RT’s colorspace conversion will change all three channels to conform to the output profile. If you open that TIFF in some program that doesn’t use an internal working profile, you’ll probably be looking at a histogram based on the raw TIFF image, which will be different. Or, if you open the TIFF in a program that does convert to a different internal working profile, the histogram will be different.
I don’t know the RT particulars, but I’d surmise the difference you’re seeing is due to the colorspace conversions, not the per-channel curve. Keep in mind that the color management system is supposed to maintain a consistent image perceptually, but the actual RGB values needed to do that will change as the image works its way through the gonkulator…