The focus of this work is to comprehensively understand hydro-dynamical back-flows and their role in dynamics and non-thermal spectral signatures particularly during the initial phase of X-shaped radio galaxies. In this regard, we have performed axisymmetric (2D) and three dimensional (3D) simulations of relativistic magneto-hydrodynamic jet propagation from tri-axial galaxies. High-resolution dynamical modelling of axisymmetric jets has demonstrated the effect of magnetic field strengths on lobe and wing formation. Distinct X-shape formation due to back-flow and pressure gradient of ambient is also observed in our 3D dynamical run. Furthermore, the effect of radiative losses and diffusive shock acceleration on the particle spectral evolution is demonstrated, which particularly highlights how crucial their contributions are in the emission signature of these galaxies. This imparts a significant effect on the galaxy's equipartition condition, indicating that one must be careful in extending its use in estimating other parameters, as the criterion evolves with time.