Patients with superior canal dehiscence (SCD) suffer from events of dizziness and vertigo in response to sound, also known as Tullio phenomenon (TP). The present work seeks to explain the fluid-dynamical mechanisms behind TP. In accordance with the so-called third window theory, we developed a computational model for the vestibular signal pathway between stapes and SCD. It is based on first principles and accounts for fluid-structure interactions arising between endolymph, perilymph, and membranous labyrinth. The simulation results reveal a wave propagation phenomenon in the membranous canal, leading to two flow phenomena within the endolymph which are in close interaction. First, the periodic deformation of the membranous labyrinth causes oscillating endolymph flow which forces the cupula to oscillate in phase with the sound stimulus. Second, these primary oscillations of the endolymph induce a steady flow component by a phenomenon known as steady streaming. We find that this steady flow of the endolymph is typically in ampullofugal direction. This flow leads to a quasi-steady deflection of the cupula which increases until the driving forces of the steady streaming are balanced by the elastic reaction forces of the cupula, such that the cupula attains a constant deflection amplitude which lasts as long as the sound stimulus. Both response types have been observed in the literature. In a sensitivity study, we obtain an analytical fit which very well matches our simulation results in a relevant parameter range. Finally, we correlate the corresponding eye response (vestibulo-ocular reflex) with the fluid dynamics by a simplified model of lumped system constants. The results reveal a "sweet spot" for TP within the audible sound spectrum. We find that the underlying mechanisms which lead to TP originate primarily from Reynolds stresses in the fluid, which are weaker at lower sound frequencies.