The incorporation of molecular switches on nanodevices requires both the intactness of the molecule once deposited on a substrate and the persistence of the reversible switching feature. Recently, the reversible spin-switching of strapped Ni(II)-porphyrin complexes deposited on Ag(111) surface is demonstrated with low-temperature scanning tunneling microscopy (STM). The spin transition is accompanied by the coordination change of the metal center, a phenomenon denominated in coordination-induced spin-state switching (CISSS). In this contribution, the spin switching of the deposited strapped Ni-porphyrin molecules using different quantum chemistry approaches is explored. This calculations inform about the geometry and electronic structure of the adsorbed molecules and the origin of the voltage-dependent switching promoted by the STM tip. Two different mechanisms are inspected to elucidate the key role of the tip, mainly the electron injection between the tip and the molecule and the differential stabilization of the two spin states by the applied electric field between the tip and the silver surface. This study puts in evidence the relevance of the pyridine ligand contained in the strap in the transport properties as in the CISSS process itself.