Novel spectropolarimetric observations of the He I multiplet are used to explore the dynamics of the chromospheric oscillation above sunspot umbrae. The results presented here provide strong evidence in support of the two-component model proposed by Socas-Navarro and coauthors. According to this model, the waves propagate only inside channels of subarcsecond width (the ``active'' component), whereas the rest of the umbra remains nearly at rest (the ``quiet'' component). Although the observations support the fundamental elements of that model, there is one particular aspect that is not compatible with our data. We find that, contrary to the scenario as originally proposed, the active component remains through the entire oscillation cycle and harbors both the upflowing and the downflowing phase of the oscillation.