Currently, multiple emulsions via liquid-liquid phase separation in ternary polymer solutions have sparked considerable interest because of its remarkable potential in physical, medical, and biological applications. The transient "onion-like" multilayers are highly dependent on the evolution kinetics, which is challenging to be scrutinized in experiments and has not yet been fully understood. Here, we report a thermodynamically consistent multicomponent Cahn-Hilliard model to investigate the kinetics of multiple emulsions by tracing the temporal evolution of the local compositions inside the emulsion droplets. We reveal that the mechanism governing the kinetics is attributed to the competition between surface energy minimization and phase separation. Based on this concept, a generalized morphology diagram for different emulsion patterns is achieved, showing a good accordance with previous experiments. Moreover, combining the analysis for the kinetics and the morphology diagram, we predict new emulsion structures that provide general guidelines to discovery, design, and manipulation of complex multiphase emulsions.