We present theoretical and experimental results showing the effects of incoherent population mixing on two-dimensional (2D) coherent excitation spectra that are measured via a time-integrated population and phase-sensitive detection. The technique uses four collinear ultrashort pulses and phase modulation to acquire two-dimensional spectra by isolating specific nonlinear contributions to the photoluminescence or photocurrent excitation signal. We demonstrate that an incoherent contribution to the measured line shape, arising from nonlinear population dynamics over the entire photoexcitation lifetime, generates a similar line shape to the expected 2D coherent spectra in condensed-phase systems. In those systems, photoexcitations are mobile such that inter-particle interactions are important on any time scale, including those long compared with the 2D coherent experiment. Measurements on a semicrystalline polymeric semiconductor film at low temperatures show that, in some conditions in which multi-exciton interactions are suppressed, the technique predominantly detects coherent signals and can be used, in our example, to extract homogeneous line widths. The same method used on a lead-halide perovskite photovoltaic cell shows that incoherent population mixing of mobile photocarriers can dominate the measured signal since carrier-carrier bimolecular scattering is active even at low excitation densities, which hides the coherent contribution to the spectral line shape. In this example, the intensity dependence of the signal matches the theoretical predictions over more than two orders of magnitude, confirming the incoherent nature of the signal. While these effects are typically not significant in dilute solution environments, we demonstrate the necessity to characterize, in condensed-phase materials systems, the extent of nonlinear population dynamics of photoexcitations (excitons, charge carriers, etc.) in the execution of this powerful population-detected coherent spectroscopy technique.