  We investigate gradual development of the quasiparticle states in two quantum
dots attached to opposite sides of the topological superconducting nanowire,
hosting the boundary modes. Specifically, we explore the non-equilibrium
cross-correlations transmitted between these quantum dots via the zero-energy
Majorana modes. From the analytical and numerical results we reveal nonlocal
features in the transient behavior of electron pairing, which subsequently
cease while the hybrid structure evolves towards its asymptotic steady limit
configuration. We estimate duration of these temporary nonlocal phenomena and
inspect their possible manifestation in the quench-driven processes. Such
dynamical effects might play an important role in braiding protocols of the
topological and/or conventional superconducting quantum bits using nanoscopic
hybrid structures.
