Umbral chromospheric oscillations exhibit significant differences compared to their photospheric counterparts. We evaluate two competing scenarios proposed for explaining those observations: a chromospheric resonant cavity and waves traveling from the photosphere to upper atmospheric layers. The oscillatory signatures of both models have been determined from numerical simulations, and they have been compared to observations. We find that a high-frequency peak in the He I 10830 Å power spectra cannot discriminate between both theories, contrary to the claims of Jess et al. (2019). In contrast, phase differences between velocity and temperature fluctuations reveal a standing pattern and unequivocally prove the presence of an acoustic cavity above umbrae. Our findings offer a new seismic method to probe sunspot chromospheres through the identification of resonant nodes in phase spectra.