Time-dependent neutronics analysis for the ferritic steel first wall of the HIBALL heavy ion beam fusion reactor conceptual design is presented. Neutron target interactions that lead to spectrum softening and neutron multiplication are accounted for. The time-of-flight (TOF) spread of neutrons within each energy group is considered. Neutron slowing down in the INPORT first-wall protection system, which is similar to the HYLIFE concept, is found to significantly affect the time over which the damage occurs in the first wall. In the case of an unprotected wall, the time spread is determined primarily by the TOF spread. The INPORT concept is found to significantly reduce both average and peak instantaneous rates of displacements per atom, helium production, and energy deposition in the first wall.