Time-resolved spectroscopy provides the main tool for analyzing the dynamics of excitonic energy transfer in light-harvesting complexes. Inferring the time scales and effective coupling parameters from experimental data requires the development of numerically exact theoretical models. The finite duration of the laser molecule interactions and the reorganization process during the exciton migration affect the location and strength of spectroscopic signals. We show that the nonperturbative hierarchical equations of motion method captures these processes in a model exciton system, including the charge-transfer state.