Context. The use of instruments that record narrowband images at selected wavelengths is a common approach in solar observations. They allow scanning of a spectral line by sampling the Stokes profiles with two-dimensional images at each line position, but require a compromise between spectral resolution and temporal cadence. The interpretation and inversion of spectropolarimetric data generally neglect changes in the solar atmosphere during the scanning of line profiles. Aims: We evaluate the impact of the time-dependent acquisition of various wavelengths on the inversion of spectropolarimetric profiles from chromospheric lines during umbral flashes. Methods: Numerical simulations of nonlinear wave propagation in a sunspot model were performed with the code MANCHA. Synthetic Stokes parameters in the Ca II 8542 Å line in NLTE were computed for an umbral flash event using the code NICOLE. Artificial profiles with the same wavelength coverage and temporal cadence from reported observations were constructed and inverted. The inferred atmospheric stratifications were compared with the original simulated models. Results: The inferred atmospheres provide a reasonable characterization of the thermodynamic properties of the atmosphere during most of the phases of the umbral flash. The Stokes profiles present apparent wavelength shifts and other spurious deformations at the early stages of the flash, when the shock wave reaches the formation height of the Ca II 8542 Å line. These features are misinterpreted by the inversion code, which can return unrealistic atmospheric models from a good fit of the Stokes profiles. The misguided results include flashed atmospheres with strong downflows, even though the simulation exhibits upflows during the umbral flash, and large variations in the magnetic field strength. Conclusions: Our analyses validate the inversion of Stokes profiles acquired by sequentially scanning certain selected wavelengths of a line profile, even in the case of rapidly changing chromospheric events such as umbral flashes. However, the inversion results are unreliable during a short period at the development phase of the flash.