The biaxial nematic phase was recently observed in different thermotropic liquid crystals, namely bent-core compounds, side-chain polymers, bent-core dimers, and organosiloxane tetrapodes. In this work, a series of experiments with a nematic organosiloxane tetrapode where nuclear magnetic resonance (NMR) spectra are collected while the sample is continuously rotating around an axis perpendicular to the magnetic field, are discussed in conjunction with the analysis of a deuterium NMR experiment on the same system reported earlier. The sample used is a mixture of a deuterated probe with the tetrapode. The mixture exhibits a nematic range between -40 degrees C and 37 degrees C. The results of the two independent, but complementary deuterium NMR experiments confirm the existence of a biaxial nematic phase for temperatures below 0 degrees C with high values of the asymmetry parameter at low temperatures. The presence of slow movements of the tetrapode mesogenic units in the low-temperature regime could also be detected through the analysis of the NMR spectra. Simulations indicate that these movements are mainly slow molecular reorientations of the mesogenic units associated with the presence of collective modes in the nematic phases of this compound. In the case of tetrapodes, recent investigations attribute the origin of biaxiality to the hindering of reorientations of the laterally attached mesogenic units which constitute the tetrapode. This study relates the molecular movements with the nematic biaxial ordering of the system.