The new oxometalates Cs3NbO4 and Cs3TaO4 together with Cs3VO4 crystallize with the K3NO4 structure type [Pnma, a = 12.495(2) Å, b = 9.0183(14) Å, and c = 6.6529(10) Å for the V compound; a = 12.928(2) Å, b = 9.177(3) Å, and c = 6.739(4) Å for the Nb; and a = 12.963(4) Å, b = 9.122(2) Å, and c = 6.774(1) Å for the Ta compound]. Their crystal structures were evaluated on the basis of single-crystal and powder X-ray diffractometry, assisted by vibrational spectroscopy, thermoanalysis, and DFT calculations. The crystal structures contain tetrahedral [M5+O4]3- anions, representing the first occurrence of Nb and Ta in a tetrahedral oxidic environment. Many representatives of the orthorhombic K3NO4 structure type have been described in the literature with a cubic structure model with disordered O atomic positions. Based on studies on Cs3MO4 (M = P, V, Nb, or Ta), we show here three different effects which can lead to (pseudo)cubic data sets. Two of them are problems of crystallographic nature (overlooked twinning or adverse atomic form factor ratios), but the third one, phase transformation into a plastic crystalline high-temperature modification, leads to a "truly" cubic structure with dynamically disordered (freely rotating) oxometalate anions. This might be of interest with respect to a large and growing number of sulfido- and selenidometalate materials which are today in discussion as solid-state electrolytes and to the mechanism of the unusually efficient ion transport therein.