The companion of this paper, Part I, discovered the characteristics of the rainfall progression in tropical-depression (TD)-type waves over the western North Pacific. In Part II, the large-scale controls on the convective rainfall progression have been investigated using the ERA-Interim data and the TRMM 3B42 precipitation-rate data during June-October from 1998 to 2013 through budgets of moist static energy (MSE) and moisture. A buildup of column-integrated MSE occurs in advance of deep convection, and an export of MSE occurs following deep convection, which is consistent with the MSE recharge-discharge paradigm. The MSE recharge-discharge is controlled by horizontal processes, whereby horizontal moisture advection causes net MSE import prior to deep convection. Such moistening by horizontal advection creates a moist midtroposphere, which helps destabilize the atmospheric column, leading to the development of deep convective rainfall. Following the heaviest rainfall, negative horizontal moisture advection dries the troposphere, inhibiting convection. Such moistening and drying processes explain why deep convection can develop without preceding shallow convection. The advection of moisture anomalies by the mean horizontal flow controls the tropospheric moistening and drying processes. As the TD-type waves propagate northwestward in coincidence with the northwestward environmental flow, the moisture, or convective rainfall, is phase locked to the waves. The critical role of the MSE import by horizontal advection in modulating the rainfall progression is supported by the anomalous gross moist stability (AGMS), where the lowest AGMS corresponds to the quickest increase in the precipitation rate prior to the rainfall maximum.