This paper presents a detailed description, analysis, and interpretation of the spectropolarimetric observations recently reported by Socas-Navarro, Trujillo Bueno, & Ruiz Cobo. These observations consist of time series of Stokes I and V profiles above a sunspot umbra. The spectral lines observed simultaneously are the Ca II chromospheric lines at 8498 and 8542 Å and the photospheric Fe I line at 8497 Å. These spectropolarimetric observations unveil an intriguing time-dependent behavior of the Stokes V profiles in the chromospheric lines. This behavior should be considered as an observational reference for future radiation magnetohydrodynamic simulations of sunspot chromospheres. The analysis of the observed time series shows that a ``normal,'' nearly antisymmetric V profile rapidly evolves toward an ``anomalous,'' completely asymmetric profile, returning later to the normal state. The occurrence of such anomalous circular polarization profiles repeats itself with a periodicity of ~150 s. After giving arguments to discard other scenarios, we are able to interpret the anomalous V profiles as a consequence of the development of a second unresolved atmospheric component. This unresolved component seems to be the same that produces the umbral flashes observed in other sunspots, where it is present with a larger filling factor. Based on observations obtained with the Gregory Coudé Telescope, operated on the island of Tenerife by the Observatory of Göttingen University, in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias.