Surface-directed phase separation via a two-step quench process in asymmetry polymer mixtures is numerically investigated by coupling the Flory-Huggins-de Gennes equation with the Cahn-Hilliard-Cook equation. Two distinct situations, i.e., the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed, respectively. The morphology and evolution dynamics of the phase structure, especially the secondary domain structure, are analyzed. The wetting layer formation mechanisms during the two-step quench process are examined. The simulated results demonstrate that different secondary domain structures in these two situations can be induced by the second quench with deeper quench depth, which can be used to tailor phase morphology. It is also found that, in the second quench process, the evolution of the wetting layer thickness can cross over to a faster growth when the preferential component is the minority component. In this situation, the formation mechanism of the wetting layer will change and is eventually determined by the second quench depth. However, when the preferential component is the majority component, a deeper second quench depth corresponds to a slower growth of the wetting layer thickness. The chemical potential is calculated to explain the difference regarding the growth dynamics of the wetting layer thickness between these both situations.