Abstract Galaxy intrinsic alignments (IAs) have long been recognised as a significant contaminant to weak lensing-based cosmological inference. In this paper we seek to quantify the impact of a common modelling assumption in analytic descriptions of intrinsic alignments: that of spherically symmetric dark matter halos. Understanding such effects is important as the current generation of intrinsic alignment models are known to be limited, particularly on small scales, and building an accurate theoretical description will be essential for fully exploiting the information in future lensing data. Our analysis is based on a catalogue of 113,560 galaxies between z = 0.06 − 1.00 from MassiveBlack-II, a hydrodynamical simulation of box length 100h−1 Mpc. We find satellite anisotropy contributes at the level of $\ge 30-40\%$ to the small scale alignment correlation functions. At separations larger than 1h−1 Mpc the impact is roughly scale-independent, inducing a shift in the amplitude of the IA power spectra of $∼ 20\%$. These conclusions are consistent across the redshift range and between the MASSIVEBLACK-II and ILLUSTRIS simulations. The cosmological implications of these results are tested using a simulated likelihood analysis. Synthetic cosmic shear data is constructed with the expected characteristics (depth, area and number density) of a future LSST-like survey. Our results suggest that modelling alignments using a halo model based upon spherical symmetry could potentially induce cosmological parameter biases at the ∼1.5σ level for S8 and w.