The Monte-Carlo simulated response for γ-ray detection of the FAst TIMing Array (FATIMA) for exploitation within the DEcay SPECtroscopy (DESPEC) experimental system at the FAIR Phase-0 facility at Darmstadt, Germany is presented. In this configuration, FATIMA consisted of 36 LaBr3(Ce) detectors surrounding the AIDA, position-sensitive charged-particle active stopper. The decay of the Iπ=8+ isomer-fed decay cascade in 96Pd, measured in the first DESPEC experiment at the FAIR-0 facility was used to validate the simulations. The experimental data yielded in-situ full-energy peak efficiency values for FATIMA of 11.2(11)%, 6.8(7)%, 3.8(4)% and 2.1(4)% at 106, 325, 684 and 1415 keV respectively, consistent with the values derived from the simulated response.