  In this communication we consider generalities of the proximity effect in a
contact between a conventional $s$-wave superconductor (S) nano-island and a
thin film of a topological insulator (TI). A local hybridization coupling
mechanism is considered and a corresponding model is corroborated that captures
not only the induced unconventional superconductivity in a TI, but also
predicts the spreading of topologically protected surface states into the
superconducting over-layer. This dual nature of the proximity effect leads
specifically to a modified description of topological superconductivity in
these systems. Experimentally accessible signatures of this phenomenon are
discussed in the context of scanning tunneling microscopy measurements. For
this purpose an effective density of states is computed in both the
superconductor and topological insulator. As a guiding example, practical
applications are made for Nb islands deposited on a surface of Bi$_2$Se$_3$.
The obtained results are general and can be applied beyond the particular
material system used. Possible implications of these results to proximity
circuits and hybrid hardware devices for quantum computation processing are
discussed.
