In pump-probe time and angle-resolved photoemission spectroscopy (TR-ARPES) experiments the presence of the pump pulse adds a new level of complexity to the photoemission process in comparison to conventional ARPES. This is evidenced by pump-induced vacuum space-charge effects and surface photovoltages, as well as multiple pump excitations due to internal reflections in the sample-substrate system. These processes can severely affect a correct interpretation of the data by masking the out-of-equilibrium electron dynamics intrinsic to the sample. In this study, we show that such effects indeed influence TR-ARPES data of graphene on a silicon carbide (SiC) substrate. In particular, we find a time- and laser fluence-dependent spectral shift and broadening of the acquired spectra, and unambiguously show the presence of a double pump excitation. The dynamics of these effects is slower than the electron dynamics in the graphene sample, thereby permitting us to deconvolve the signals in the time domain. Our results demonstrate that complex pump-related processes should always be considered in the experimental setup and data analysis. (C) 2015 Elsevier B.V. All rights reserved.