Context. Several instances of low-frequency quasi-periodic oscillations (QPOs) have been reported for ultraluminous X-ray sources (ULXs), including three observed for pulsating ULXs (PULXs) to date. The nature of various ULXs and the detailed properties of accretion in PULXs remain unclear. Aims. We seek to determine if there exists a QPO model that fits the data and we investigate whether mHz QPOs can be used to constrain the magnetic field and accretion rate of the neutron stars in PULXs. Furthermore, we consider whether all the low-frequency QPOs in ULXs can be interpreted as a manifestation of the same phenomenon. Methods. The available data indicates that the mHz QPO frequency is inversely proportional to the neutron star rotational period in PULXs. We examined two different physical models that could potentially explain this frequency-period dependence: 1) a precession of the inner accretion disk and torus in the strong gravity of a spinning neutron star and 2) inner disk precession forced by the neutron star magnetic field. In the latter case, we applied a magnetic precession model to the PULX data, with the magnetic threading of the accretion disk constrained by recent simulations. Results. Based on the magnetic precession model and on recent progress in the study of the inner structure of accretion disks, we predict an inverse scaling of QPO frequency with the neutron star period in PULXs. The theoretical curve is largely independent of the stellar magnetic field or mass accretion rate and agrees with the data for the known QPOs in PULXs. Alternatively, precession of strong-gravity origin would imply a restrictive upper limit on the stellar magnetic dipole. The flat-top noise QPOs detected in (non-pulsating) ULXs display observational properties that appear to be very different from the QPOs detected in PULXs, indicating they might have different origins.