Pump-probe microscopy of melanin in tumors has been proposed to improve diagnosis of malignant melanoma, based on the hypothesis that aggressive cancers disaggregate melanin structure. However, measured signals of melanin are complex superpositions of multiple nonlinear processes, which makes interpretation challenging. Polarization control during measurement and data fitting are used to decompose signals of melanin into their underlying molecular mechanisms. We then identify the molecular mechanisms that are most susceptible to melanin disaggregation and derive false-coloring schemes to highlight these processes in biological tissue. We demonstrate that false-colored images of a small set of melanoma tumors correlate with clinical concern. More generally, our systematic approach of decomposing pump-probe signals can be applied to a multitude of different samples.