A layer of mulch over the roots of newly transplanted trees and shrubs keeps the soil from compacting so tender roots get a faster start. But colored mulch is not in that category. And it has nothing to do with the hue. Colored mulches are made from shredded, recycled waste wood, primarily pallets and shipping crates. Since the dyes will only penetrate freshly-shredded wood, coating composted bark with the decorative pigment is not an option.
Gardeners know what freshly-ground wood chips do to their plants.
They steal nitrogen from the soil, depriving roots of this most important nutrient. Plants literally starve to death. The process through which this occurs is fairly complex and involved the relative amounts of carbon and nitrogen present in each product. Dyed wood is mostly carbon. As a host of micro-organisms in the soil goes to work digesting it, they suck almost all available nitrogen from the top 2 to 3 inches of soil.