  We use zoom hydrodynamical simulations to investigate the properties of
satellites within galaxy-sized dark-matter haloes with different assembly
histories. We consider two classes of haloes at redshift $z=0$: `stalled'
haloes that assembled at $z>1$ and `accreting' ones that are still forming
nowadays. Previously, we showed that the stalled haloes are embedded within
thick filaments of the cosmic web while the accreting ones lie where multiple
thin filaments converge. We find that satellites in the two classes have both
similar and different properties. Their mass spectra, radial count profiles,
baryonic and stellar content, and the amount of material they shed are
indistinguishable. However, the mass fraction locked in satellites is
substantially larger for the accreting haloes as they experience more mergers
at late times. The largest difference is found in the satellite kinematics.
Substructures fall towards the accreting haloes along quasi-radial trajectories
whereas an important tangential velocity component is developed, before
accretion, while orbiting the filament that surrounds the stalled haloes. Thus,
the velocity anisotropy parameter of the satellites ($\beta$) is positive for
the accreting haloes and negative for the stalled ones. This signature enables
us to tentatively categorize the Milky Way halo as stalled based on a recent
measurement of $\beta$. Half of our haloes contain clusters of satellites with
aligned orbital angular momenta corresponding to flattened structures in space.
These features are not driven by baryonic physics and are only found in haloes
hosting grand-design spiral galaxies, independently of their assembly history.
