Nuclear dynamics is investigated theoretically from first principles by employing the ab initio vibronic models of the prototypical naphthalene and anthracene radical cations developed in Part I. This Part is primarily aimed at corroborating a large amount of available experimental data with a specific final goal to establish an unambiguous link with the current observations in astrophysics and astronomy. The detailed analyses presented here perhaps establish that these two prototypical polycyclic aromatic hydrocarbon radical cations are indeed potential carriers of the observed diffuse interstellar bands.