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 consider two questions: the stability of the PMLs in corners and the energy estimates for the PML systems in the time domain. Based on the Fourier analysis, we deduce necessary and sufficient conditions of stability of the newly constructed PMLs in corners. The obtained results are confirmed with the help of the numerical experiments. In order to obtain explicit energy estimates for the PML system in the time domain, we make 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.