The viscous fingering morphologies at a particular stage of emulsion displacements are observed to follow similar development patterns as that of the partially-miscible viscous fingering behavior (existent between the commonly studied fully miscible and immiscible systems). Chemically-induced viscous fingering before and after the finger droplet development resembling the partially-miscible fluid behavior is investigated using fractal dimensions and various -classic and modified- dimensionless scaling groups. We demonstrate, through the quantitative analysis using the empirical data collected from our previous experimental study, that the finger droplet formation morphologies observed in partially-miscible injection are indicative of an emulsion hydrodynamic instability behavior. The dominant parameters responsible for such droplet formation and their relationship to fractal dimension and hydrodynamic stability are mapped in a phase diagram with the original experimental images.