Phase modulation and phase cycling schemes have been commonly used in electronic two-dimensional (2D) spectroscopy where the observables are incoherent signals such as fluorescence or photocurrent. Although the methods have distinct advantages compared to the coherent signal-detected 2D spectroscopy in sensitivity, possibility to measure spectra from isolated quantum systems and direct visualization of the contributions from the different states to the action signals, and ambiguities in interpreting the spectra have emerged. Recent reports have shown that apart from the nonlinear signals from the four pulse interactions, mixing of the linear signals due to nonlinear population dynamics during the long measurement time of the action signals can also contribute to the measured 2D spectra. Exciton exciton annihilation has been considered to play a major role in the mixing of the linear signals. Thus, it has become important to further characterize the origin of the measured signals. Here, using a nonperturbative simulation of the 2D spectra based on the time evolution of the density matrix in the Lindblad form, we show that the exciton-exciton annihilation contributes to the measured signal only if the quantum yields of the different excited states are not the same. In these cases, the mixed signals can be distinguished from the true nonlinear signals if the phases are measured with respect to the linear signals. In action-detected 2D spectra, the mixed signals have a pi phase shift relative to the true nonlinear signals. A detailed discussion on the experimental implementations of the schemes used in the simulations is also provided.