Should an ICC profile correct an image with a colour cast?
A. A profile should not correct anything in an image. Thus if you have an original with a cast the print should also have that cast. Correcting the image is a separate stage in the reproduction process from applying the profile. What the input profile does is to tell you what CIELAB values were seen by the scanner to get a particular set of RGB values. So, when the scanner gets a specific set of RGB values for any pixel the software uses this formula to determine the CIELAB values that it saw for that pixel on the original. The output profile then defines the CMYK values needed to reproduce that colour. So, any cast in the image will be retained in the reproduction. The removal of colour casts from an image needs separate software.