Kinetic Monte Carlo (KMC) simulations have emerged as an important tool to help improve the efficiency of organic electronic devices by providing a better understanding of their device physics. In the KMC simulation of an organic device, the reliability of the results depends critically on the accuracy of the chosen charge-transfer rates, which are themselves strongly influenced by the site-energy differences. These site-energy differences include components coming from the electrostatic forces present in the system, which are often evaluated through electric potentials described by the Poisson equation. Here we show that the charge-carrier self-interaction errors that appear when evaluating the site-energy differences can lead to unreliable simulation results. To eliminate these errors, we propose two approaches that are also found to reduce the impact of finite-size effects. As a consequence, reliable results can be obtained at reduced computational costs. The proposed methodologies can be extended to other device simulation techniques as well.