  Many accreting black holes and neutron stars exhibit rapid variability in
their X-ray light curves, termed quasi-periodic oscillations (QPOs). The most
commonly observed type is the low-frequency ($\lesssim 10$ Hz), type-C QPO,
while only a handful of sources exhibit high-frequency QPOs ($\gtrsim 60$ Hz).
The leading model for the type-C QPO is Lense-Thirring precession of a hot,
geometrically thick accretion flow that is misaligned with the black hole's
spin axis. However, existing versions of this model have not taken into account
the effects of a surrounding, geometrically thin disc on the precessing, inner,
geometrically thick flow. In Bollimpalli et. al 2023, using a set of GRMHD
simulations of tilted, truncated accretion discs, we confirmed that the outer
thin disc slows down the precession rate of the precessing torus, which has
direct observational implications for type-C QPOs. In this paper, we provide a
detailed analysis of those simulations and compare them with an aligned
truncated disc simulation. We find that the misalignment of the disc excites
additional variability in the inner hot flow, which is absent in the comparable
aligned-disc simulations. This suggests that the misalignment may be a crucial
requirement for producing QPOs. We attribute this variability to global
vertical oscillations of the inner torus at epicyclic frequencies corresponding
to the transition radius. This explanation is consistent with current
observations of higher frequency QPOs in black hole X-ray binary systems.
