Post-ionization fragmentation of small ionic krypton clusters, Kr (N = 3-13), has been investigated using a semiclassical non-adiabatic dynamics approach consisting of classical treatment of atomic nuclei and full quantum treatment of electrons, and an extended diatomics-in-molecules model including the spin-orbit coupling as well as leading three-body interaction corrections. Electronic quantum decoherence has also been considered via a simplified scheme proposed previously. The positive charge has been initially localized on a randomly selected atom in the form of a localized P positive hole. It follows from the calculations that the data are not converged at timescales usually considered in dynamical calculations (t = 200 ps in this work) and that an extension to t ≈ 1 μs is needed. An approximate multi-scale treatment developed recently has been used to provide such an extension of the output of dynamical calculations. A qualitative agreement with available experimental data has been achieved, in particular, the experimental observation that the monomer fragment, Kr, completely dominates has been reproduced. Interestingly, stabilized neutral dimer and trimer fragments have been observed in our calculations at non-negligible abundances despite extremely weak bonding in these species.