In order to properly simulate cases in which gyrotrons exhibit fast temporally varying oscillations, such as non-stationary oscillations or possible dynamic After-Cavity Interaction (ACI), an adequate model for the beam-wave interaction has to be used. We will show that the commonly used assumption of considering a constant wave-field envelope during the electron transit time has to be abandoned. The appropriate model (reduced 1D Particle-In-Cell (PIC) model) is briefly presented and the implications of using an inadequate model are illustrated. For the case of a 150W/260GHz gyrotron, non-stationary simulations with the new model will be compared to experiment and used in order to investigate the underlying mechanism of these oscillations.