In a standard test piece (plastic dumbbell for materials testing) this is usually a single wall section and unlikely to demonstrate any significant warpage.
The issue with warp associated with color pigments is most likely to be seen in semi-crystalline materials where different pigments can affect the crystalline growth and will demonstrate both size and warp differences which are clearly seen in existing tooling, and therefore, is also affected by the part geometry and the quality of the tool build to be able control the uniformity and rate of the cooling.
In light of the above particle size and dispersion also play there part. These aspects the pigment manufacturer should be able to give some help with, and of course some of the big materials manufacturers have their own labs that will have done some work on their materials, that can often be a good source of guidance.
If you design your part and tool with the understanding of what areas are critical to the distortion of the product and eliminate or design out the issues the effects of the pigment on the product will be minimized.
Most organic pigment manufacturers uses their own test method and most of them are molding a chip in a homogeny thickness with a certain length and width (longer length) and then measures the shrinkage in length vs transverse direction to provide what could be called a warping index. The uniso-tropical shrinkage is a sign of warping and an iso-tropical index of 1 is of course the best (= same shrinkage in length as well as in transverse direction).
All pigments act as nucleators and will influence shrinkage and warping in semi crystalline resins. Some organic pigment chemistries are really powerful nucleators and will provide a high degree of warping (e.g. Phtalocyanine pigments). Besides general aspect as part- and mold design and a careful selection of pigments, nucleating agents may be added to overcome warping effects.