in SiLENSe "Fermi level" means "quasi-Fermi level" throughout the program, documentation, and supporting materials.
The relative position of the Fermi level and the edge of the respective band (conduction or valence) depends on the carrier concentration. In fact, the Fermi level is just another variable for the carrier concentration. All the respective equations can be found in Sec. 3 of SiLENSe Physics Summary.
At low carrier concentration, hole Fermi level is above the valence band edge. When the hole concentration increases, the difference becomes lower and eventually Fermi level becomes lower that the valence band edge. The difference (Fp-Ev) depends on the acceptor ionization energy and the valence band density of states. The qualitative difference between red LEDs and blue LEDs is a dramatically higher acceptor activation energy in III-nitrides.