  We study the dynamics of the quantum Dyson hierarchical model in its
paramagnetic phase. An initial state made by a local excitation of the
paramagnetic ground state is considered. We provide analytical predictions for
its time evolution, solving the single-particle dynamics on a hierarchical
network. A localization mechanism is found and the excitation remains close to
its initial position at arbitrary times. Furthermore, a universal scaling among
space and time is found related to the algebraic decay of the interactions as
$r^{-1-\sigma}$. We compare our predictions to numerics, employing tensor
network techniques, for large magnetic fields, discussing the robustness of the
mechanism in the full many-body dynamics.
