  Inspired by the physics of rare earth nickelates, we study the photoemission
(PES) and resonant inelastic X-ray scattering (RIXS) spectra of a correlated
electron system with two types of insulating sublattices. Sublattice A is
characterized by a hybridization gap and a low-spin state, while sublattice B
features a Mott gap and a local magnetic moment. We show how the coupling of
these two qualitatively different insulating states affects the dynamics of
photo-induced charge carriers and how the nonequilibrium states manifest
themselves in the PES and RIXS signals. In particular, we find that charge
carriers created on the B sublattice migrate to the A sublattice, where they
contribute to the creation of in-gap states in the PES signal, and to
characteristic peaks in the nonequilibrium RIXS spectrum. While the
contributions from the two sublattices cannot be easily distinguished in the
local photoemission spectrum, the weights of the RIXS signals in the
two-dimensional $\omega_\text{in}$-$\omega_\text{out}$ space provide
information on the local state evolution on both sublattices.
