  The magnetic sublayers introduced by intercalation into the host
transition-metal dichalcogenide (TMD) are known to produce various magnetic
states. The magnetic sublayers and their magnetic ordering strongly modify the
electronic coupling between layers of the host compound. Understanding the
roots of this variability is a significant challenge. Here we employ the
angle-resolved photoelectron spectroscopy at various photon energies, the {\it
ab initio} electronic structure calculations, and modeling to address the
particular case of Ni-intercalate, Ni$_{1/3}$NbS$_2$. We find that the bands
around the Fermi level bear the signature of a strong yet unusual hybridization
between NbS$_2$ conduction band states and the Ni 3$d$ orbitals. The
hybridization between metallic NbS$_2$ layers is almost entirely suppressed in
the central part of the Brillouin zone, including the part of the Fermi surface
around the $\mathrm{\Gamma}$ point. Simultaneously, it gets very pronounced
towards the zone edges. It is shown that this behavior is the consequence of
the rather exceptional, {\it symmetry imposed}, spatially strongly varying,
{\it zero total} hybridization between relevant Ni magnetic orbitals and the
neighboring Nb orbitals that constitute the metallic bands. We also report the
presence of the so-called $\beta$-feature, discovered only recently in two
other magnetic intercalates with very different magnetic orderings. In
Ni$_{1/3}$NbS$_2$, the feature shows only at particular photon energies,
indicating its bulk origin. Common to prior observations, it appears as a
series of very shallow electron pockets at the Fermi level, positioned along
the edge of the Brillouin zone. Unforeseen by {\it ab initio} electronic
calculations, and its origin still unresolved, the feature appears to be a
robust consequence of the intercalation of 2H-NbS$_2$ with magnetic ions.
