A series of core–shell heterostructures consisting of the spin transition Prussian blue analogue Rb_aCo_b[Fe(CN)₆]_c·mH₂O (RbCoFe–PBA) as core with different shell thicknesses of K_jNi_k[Co(CN)₆]_l·nH₂O (KNiCo-PBA) has been prepared and studied as the cores undergo both thermal and light-induced phase changes. Synchrotron powder diffraction and SQUID magnetometry indicate the intersite cooperativity of the charge transfer coupled spin transition (CTCST) in the RbCoFe–PBA core decreases while the extent of lattice contraction is reduced relative to the uncoated particles. Isothermal relaxation measurements from the photo-induced high-spin (HS) state to the low-spin (LS) ground state of the RbCoFe–PBA core show that the energy barrier of the HS to LS transition dramatically decreases when adding the KNiCo-PBA shells, becoming smaller when the shell is thicker. The RbCoFe–PBA@KNiCo-PBA series is unique because the lattice parameter of KNiCo-PBA grown on the high-spin RbCoFe–PBA core particle is expanded relative to its equilibrium lattice parameter. As a result, the lattice mismatch is relieved during the spin transition. Analysis of the structural microstrain in both core and shell during the CTCST process reveals the different mechanisms by which the heterostructure accommodates the strain.