The effect of the nuclear core dynamics on the binding energies of A hypemuclei is studied in the framework of variational correlated wave functions. In addition to the core energy and to a A single-particle contribution cA, we exhibit a rearrangement energy ER which in particular depends on the AN correlations F and on the difference 8ON between the core wave function and its exact ground-state value. ER is nonzero only if there are both AN correlations (F 4: 1) and if ~ON v~ 0. The latter can result from core polarization by the A or from errors in the ground-state variational wave function of the core. ER varies linearly with 6~N for small 8ON. Detailed numerical results for central AN and NN potentials with repulsive cores confirm these general features. For a given core wave function AN correlations reduce the radius of the core nucleons relative to their c.m.; however ER leads to an expansion of the core rather than to a contraction with only CA. The core polarization energy is quite small ~ 0.4 MeV. We study the effects of errors in the variational core wave function by detuning this as a function of one of the variational parameters.