The EXPERT setup located at the Super-FRS facility, the part of the FAIR complex in Darmstadt, Germany, is intended for investigation of properties of light exotic nuclei. One of its modules, the high granularity neutron detector NeuRad assembled from a large number of the scintillating fiber is intended for registration of neutrons emitted by investigated nuclei in low-energy decays. Feasibility of the detector strongly depends on its timing properties defined by the spatial distribution of ionization, light propagation inside the fibers, light emission kinetics and transition time jitter in the multi-anode photomultiplier tube. The first attempt of understanding the pulse formation in the prototype of the NeuRad detector by comparing experimental results and Monte Carlo (MC) simulations is reported in this paper.