Optical event horizons in fibers, driven by coherent pumps, have been a prominent subject of study within the field of nonlinear optics. Previously, optical event horizons involving a potent pump and a linear-wave were interpreted as phase-matching processes wherein new spectral components are derived from the linear-wave due to the influence of the strong pump. This nonlinear interaction, coupled with the wave mixing mechanism, has been elaborated upon in the spectral domain. It's portrayed as a cascaded four-wave mixing process, achieving quasi-phase-matching through intermediate spectral components. Until now, research focused on event horizons or soliton linear-wave interactions has predominantly relied on coherent laser pump sources. However, there has been a recent resurgence in the exploration of incoherently pumped nonlinear optics. While the specific dynamics of incoherent light fields and their subsequent nonlinear processes might be elusive due to their inherent random field fluctuations, their incoherent nature unveils a multitude of statistical dynamics for nonlinear phenomena. In this work, we delve into optical event horizons encountered by linear-waves propelled by an incoherent light field within nonlinear optical fibers. Our numerical analysis scrutinizes the dynamics of linear-waves during optical event horizons under incoherent pumping. We further dissect the temporal statistics of the newly birthed idler-waves emerging from these event horizon processes.