Context. The anisotropic distribution of satellites around the central galaxy of their host halo is both well-documented in observations and predicted by the ΛCDM model. However its amplitude, direction and possible biases associated to the specific dynamics of such satellite galaxies are still highly debated. Aims. Using the cosmological hydrodynamics simulation Horizon-AGN, we aim to quantify the anisotropy of the spatial distribution of satellite galaxies relative to their central counterpart and explore its connexion to the local cosmic web, in the redshift range between 0.3 and 0.8. Methods. Haloes and galaxies were identified and their kinematics computed using their dark matter and stellar particles respectively. Sub-haloes were discarded and galaxies lying within 5 R_vir of a given halo are matched to it. The filamentary structure of the cosmic web was extracted from the density field – smoothed over a 3 h⁻¹ Mpc typical scale – as a network of contiguous segments. We then investigated the distribution function of relevant angles, most importantly the angle α between the central-to-satellite separation vector and the group’s nearest filament, aside with the angle between this same separation and the central minor axis. This allowed us to explore the correlations between filamentary infall, intra-cluster inspiralling and the resulting distribution of satellites around their central counterpart. Results. We find that, on average, satellites tend to be located on the galactic plane of the central object. This effect is detected for central galaxies with a stellar mass larger than 10¹⁰ M_⊙ and found to be strongest for red passive galaxies, while blue galaxies exhibit a weaker trend. For galaxies with a minor axis parallel to the direction of the nearest filament, we find that the coplanarity is stronger in the vicinity of the central galaxy, and decreases when moving towards the outskirts of the host halo. By contrast, the spatial distribution of satellite galaxies relative to their closest filament follows the opposite trend: their tendency to align with them dominates at large distances from the central galaxy, and fades away in its vicinity. In that redshift range, we find hints that massive red centrals with a spin perpendicular to their filament also have corotating satellites well aligned with both the galactic plane and the filament. On the other hand, lower-mass blue centrals with a spin parallel to their filament have satellites flowing straight along this filament, and hence orthogonally to their galactic plane. The orbit of these satellites is then progressively bent towards a better alignment with the galactic plane as they penetrate the central region of their host halo. Conclusions. The kinematics previously described are consistent with satellite infall and spin build-up via quasi-polar flows, followed by a re-orientation of the spin of massive red galaxies through mergers.