In this letter, we report that the source and channel Fermi-Dirac distributions in interband-tunneling-controlled transistors play a fundamental role on the modulation of the injected current. We explain the superlinear onset of the output characteristics based on the occupancy function modulation. Thus, we point out that, along with the tunneling barrier transparency, the availability of carriers and empty states, at the beginning and at the end of the tunneling path, respectively, should be always taken into account for a proper modeling of tunnel FETs.