Little is known about the role of network rigidity in light-induced structural rearrangements in network glasses due to a lack of supporting experiments and theories. In this article, we demonstrate for the first time the ultrafast structural rearrangements manifested as induced absorption (IA) over a broad spectral range in a-GexAs35-xSe65 thin films above the mean-field rigidity percolation transition, quantified by the mean coordination number ⟨r⟩ = 2.40. The IA spectrum arising from self-trapped excitons, induced structural rearrangements by softening the glass network that strikingly reveal two relaxation mechanisms which differ by one order of magnitude. The fast kinetics of electron-lattice interaction occurs within 1 ps, exhibits a weak dependence on rigidity and dominates in the sub-bandgap region. In a stark contrast, the slow kinetics are associated with the structural changes in the bandgap region and depends strongly on network rigidity. Our results further demonstrate that amplitude of IA scales a linear relationship with excitation fluence which provides a unique way to induce structural rearrangements in over-coordinated network to exploit it for practical purposes. Our results modify the conventional concept of rigidity dependence of light-induced effects in network glasses, when excited with an ultrafast laser.