We present an atomistic approach, based on a realistic structure of the compound [Fe(pyrazine)][Ni(CN)4], which provides a spatiotemporal description of the spin-crossover (SCO) phenomenon. The vibronic coupling is described through an intramolecular double-well potential, whereas the elastic interactions between the Fe centers are considered by an additional spin-state-dependent potential. The model is then investigated through molecular dynamics (MD) simulations. This work is separated into two papers. Part I [S. Mi et al., Phys. Rev. B 109, 054103 (2024)] reports on the methodology used to simulate the spin transition in the bulk material. The present Part II addresses the spatiotemporal dynamics (nucleation and growth) of the spin transition in a bimorph actuator, mimicking the operation of a nanoelectromechanical device. The spin-state configuration and local strain are calculated to explore both the spatiotemporal aspects of the spin-state switching and the resulting deformation of the bimorph cantilever, as a function of the cooperativity of the SCO material and the thickness of the films. We show that the spatiotemporal dynamics deviates from a single nucleation process since additional domains can be formed due to the lattice bending, whereas the associated elastic stresses lead to longer switching times and to incomplete transitions. A comparison with classical continuum mechanical theory reveals that the latter may be no more valid in the case of systems with ultrathin films. Interestingly, due to competing effects between the spin-state switching dynamics and the natural frequencies of the cantilever, damped oscillations are observed in the spin-state fraction and in the deformation of the cantilever before reaching a stationary state.