The behavior of H isotopes in crystals is a fundamental and recurrent theme in materials physics. Especially, the information on H diffusion over a wide temperature range provides a critical insight into the quantum mechanical nature of the subject; however, this is not yet fully explored. From state-of-the-art ab initio calculations to treat both electrons and nuclei quantum mechanically, we found that the temperature dependence of H isotope diffusivities in face-centered-cubic (fcc) Pd has an unconventional "reversed S" shape on Arrhenius plots. Such irregular behavior is ascribed to the competition between different nuclear quantum effects with different temperature and mass dependencies, which leads to a peculiar situation, where the heavier tritium (H-3) diffuses faster than the lighter protium (H-1) in the limited temperature range of 80-400 K. This unveils the mechanism of anomalous crossovers between the normal and reversed isotope effects observed in the experiments at high and low temperatures.