To clarify the mechanism of cross-interfacial molecular transport and the role of subcritical cluster population in determining the kinetics of crystal nucleation, cluster dynamics calculations based on viscosity-governed rate coefficients are confronted with experiments on crystal nucleation in six stoichiometric oxide glasses (lithium disilicate, barium disilicate, two soda-lime-silica glasses, wollastonite glass, and lithium diborate). Systematic deviations are observed in the thermal activation of the measured and predicted induction times that lead to a crossover near the glass transition. Below crossover, the viscosity based induction times are higher than the experimental ones, a relation that is reversed at higher temperatures. The differences, that may amount to orders of magnitude far from the crossover temperature, cannot be removed by taking into account the size dependence of the interfacial free energy, the depletion of the monomers, or by enforcing the proper (zero) value of the free energy of monomers. Rather, it appears that while crystal nucleation and viscosity are both diffusion related processes, they are governed by different diffusion modes.