Your question may be answered differently by users of differing Pyro formulations. ABC Pyro will provide very little general green color stain (depending on the age of the Sulfite--B componant). Pyrocat will provide very little general tan stain. PMK will provide a fair amount of yellow/green general stain.
The benefit of a pyro based developer is that the stain is proportional to silver density and thus it will have the benefit of increase highlight tonal separation and increased sharpness due to "edge effects".
It is possible that your developer may be of the low general staining variety. Not knowing the exact formulation of your developer prevents knowing it's characteristics.