Absolute colorimetric differs from relative in that it does not remap the white point. So if your target color space has a different white point, you'll see it as a color cast.
Normally you don't use absolute, it's for special purposes. Relative colorimetric is the standard. It remaps 255-255-255 white to 255-255-255 white, even if going from, say, D65 to D50 or vice versa.