This article continues the stability analysis of the generalized perfectly matched layers for 2D anisotropic dispersive models studied in Part I of the work. We obtain explicit energy estimates for the PML system in the time domain, by making use of the ideas stemming from the analysis of the associated sesquilinear form in the Laplace domain. This analysis is based on the introduction of a particular set of auxiliary unknowns related to the PML, which simplifies the derivation of the energy estimates for the resulting system. For 2D dispersive systems, our analysis allows to demonstrate the stability of the PML system for a constant absorption parameter. For 1D dispersive systems, we show the stability of the PMLs with a non-constant absorption parameter.