The nature of our approach to the dynamics of critical fluctuations initiated in earlier works of this series is studied by applying it to the kinetic Ising model and anisotropic Heisenberg ferromagnets, and by including the Hamiltonian density in constructing the critical dynamical variables (CDV). In the isotropic Heisenberg magnets as well as in the anisotropic Heisenberg ferromagnets where the transverse components of spins first become critical (Matsubara-Matsuda model), the dynamics of the CDV can be asymptotically closed within themselves (that is, the energy transfer among the CDV modes dominates that between the CDV modes and other microscopic modes) if the CDV is constructed from spin densities alone. The dynamical scaling law (DSL) then holds among phenomena associated with the spin densities. For other cases studied, the dynamics cannot be closed within the chosen CDV, and then the DSL may fail among the phenomena associated with the CDV. A tentative criterion is given for the CDV where the DSL holds. In particular, the characteristic frequency in the Matsubara-Matsuda model behaves as κ3/2f with κ the inverse correlation range of spin fluctuations, which agrees with that found for the liquid helium near the λ transition by Ferrell et al. using the DSL. However, the thermal conductivities of the magnetic systems studied remain finite at the critical points. Various equal-time correlations that involve certain short wave length spin fluctuations are studied in Appendices.