The fundamental understanding of the gelation kinetics, stress relaxation and temporal evolution in colloidal filamentous gels is central to many aspects of soft and biological matter, yet a complete description of the inherent complex dynamics of these systems is still missing. By means of photon correlation imaging (PCI), we studied the gelation of amyloid fibril solutions, chosen as a model filamentous colloid with immediate significance to biology and nanotechnology, upon passage of ions through a semi-permeable membrane. We observed a linear-in-time evolution of the gelation front and rich rearrangement dynamics of the gels, the magnitude and the spatial propagation of which depend on how effectively electrostatic interactions are screened by different ionic strengths. Our analysis confirms the pivotal role of salt concentration in tuning the properties of amyloid gels, and suggests potential routes for explaining the physical mechanisms behind the linear advance of the salt ions.