Spot Color inks are opaque and Process Color inks are transparent.
What does this mean? Well, when you use Spot colors (like Pantone colors) the ink that is applied to the page on the press does not let light through to the paper and so is affected a lot less by the color of the paper. But, when using 3 or 4-color process inks, the ink is transparent (so each ink color is able to modify the light) so the light hitting the page passes through the ink, gets reflected off the page, and then passes through the ink again before it travels to your eyes. This means that the color of the paper stock plays a huge role in determining the final look of your output.
It also means that spot colors emulated on a 4-color proofing device are affected by the proofing stock much more than they will be on the final press output. Nasty!
What do I do about it? A well-made printer profile should take paper stock color into consideration but you should note that the Rendering Intent you select will or will not correct for the stock color. Choose this carefully.