Wonderful Inkscape unfortunately does not support black overprinting. You can define colors in CMYK but it will not allow values such as 40% C + 40% M + 40% Y + 100% K (Inkscape for some reason automatically converts these back to 0% C + 0% M + 0% Y + 100% K).
Left: cyan plate after importing .svg in Scribus.
Right: cyan plate after adjusting colors.
But with the help of excellent Scribus, this is easy to fix. Simply import the .svg into Scribus, and go to edit > colors. All colors in imported Inkscape illustrations, will be RGB; most likely black has ended up as 'FromSVG#000000', or 'Grey0'. Change this color from RGB to CMYK and change values to 40% C + 40% M + 40% Y + 100% K. Check in print preview and ... voilà!