The increasing demand for More than Moore devices requires epitaxy technology to keep up with the discovery and deployment of new semiconductors. An emerging technology for cost-effective, device-quality growth is magnetron sputter epitaxy, though detailed studies on the process itself remain scarce. Here, we report an extensive study on the correlation between the substrate off-cut and film quality in AlN-on-Si heteroepitaxy. Controlled reactive pulsed magnetron sputtering is used to grow epitaxial AlN(0001) films on in situ Ar plasma etched off-cut Si(111) substrates with growth rates above 1.5 nm/s. Substrate off-cut angles in the range of 0.02°-0.30° are investigated and precisely determined by high-resolution x-ray diffraction. Structural examination of the AlN films is carried out by transmission electron microscopy and high-resolution x-ray diffraction. The AlN/Si interface is well-defined and two types of AlN domains with epitaxial relationships are observed. The formation of secondary rotation domains deteriorates the crystal quality substantially. Substrates with small off-cuts, ideally no off-cut substrates, appear to be crucial for suppressing the formation of secondary domains and further result in a better overall crystal quality of AlN films. We discuss this effect in relation to the AlN/Si interface, the substrate pre-treatment, and nucleation.