Using ultrafast optical absorption spectroscopy, the room-temperature spin-state switching dynamics induced by a femtosecond laser pulse in high-quality thin films of the molecular spin-crossover (SCO) complex [Fe(HB(tz) ) ] (tz = 1,2,4-triazol-1-yl) are studied. These measurements reveal that the early, sub-picosecond, low-spin to high-spin photoswitching event, with linear response to the laser pulse energy, can be followed under certain conditions by a second switching process occurring on a timescale of tens of nanoseconds, enabling nonlinear amplification. This out-of-equilibrium dynamics is discussed in light of the characteristic timescales associated with the different switching mechanisms, i.e., the electronic and structural rearrangements of photoexcited molecules, the propagation of strain waves at the material scale, and the thermal activation above the molecular energy barrier. Importantly, the additional, nonlinear switching step appears to be completely suppressed in the thinnest (50 nm) film due to the efficient heat transfer to the substrate, allowing the system to retrieve the thermal equilibrium state on the 100 ns timescale. These results provide a first milestone toward the assessment of the physical parameters that drive the photoresponse of SCO thin films, opening up appealing perspectives for their use as high-frequency all-optical switches working at room temperature.