The linear_RIMM-RGB_v4.icc seems to be linear. If I take an image that has been converted to the linear ProPhoto space, then in PS Assign Profile the linear_RIMM-RGB_v4.icc, I can't see any change, toggling back and forth between the two profiles. I can see a change if I change the gamma a small amount with the Exposure tool.
If I take the image in linear or nonlinear ProPhoto space and Convert to Profile to the linear_RIMM-RGB_v4.icc profile, I see a change in the image when I Convert to Profile using either the Saturation or the Perceptual intent, and further changes when toggling "use black point compensation" on and off. I don't notice a change converting with the Relative Colorimetric intent, nor when toggling black point with that intent.
Since intent and black point compensation might be causing the non-linearities you observe, what are your settings when you convert to linear_RIMM-RGB_v4.icc?