I think you need a multi-layer approach. You need a layer that can impart your color, and need to find a carrier that will work with the tint. If I recall correctly, TransTint, in your picture, has a specific formulation that is not universal. It goes better into alcohol and water, if you do not have a finish that has an emulsifier in it. That has led me to tint shellac as a base for color, if I find the color not mixing in the finish. This may well be the approach you need to use. Tint first, then poly over.