Strain engineering of functional properties in epitaxial thin films of strongly correlated oxides exhibiting octahedral-framework structures is hindered by the lack of adequate misfit relaxation models. Here we present unreported experimental evidences of a four-stage hierarchical development of octahedral-framework perturbations resulting from a progressive imbalance between electronic, elastic and octahedral tilting energies in La0.7Sr0.3MnO3 epitaxial thin films grown on SrTiO3 substrates. Electronic softening of the Mn - O bonds near the substrate leads to the formation of an interfacial layer clamped to the substrate with strongly degraded magnetotransport properties, i.e. the so-called dead layer, while rigid octahedral tilts become relevant at advanced growth stages without significant effects on charge transport and magnetic ordering.