Select Raman scattering and modulated differential scanning calorimetry (DSC) experiments on specially homogenized binary Ge_xSe_100–x and Ge_xS_100–x chalcogenide glasses, supported by ab initio MD simulations are undertaken. In both chalcogenides, the glasses exhibit a super‐strong behavior (with a melt fragility index, m(x) < 20) in the 20(1)% < x < 26(1)% composition range, defining the fragility window, and with m(x) > 20 as one goes away from the fragility window. Remarkably, molecular dynamics (MD) simulations confirm the existence of the fragility window. Furthermore, in both chalcogenide glasses, the enthalpy of relaxation at T_g, ΔH_nr(x), becomes minuscule (≈0) in the 20(1)% < x < 26(1)% range, defining the reversibility window, and with ΔH_nr(x) increasing by an order magnitude abruptly with x outside that window. Thus, super‐strong melts formed in the fragility window give rise to isostatically rigid glasses in the reversibility window and fragile melts formed at x < 20(1)% and at x > 26(1)% give rise to flexible‐ and stressed‐rigid glasses, respectively. Melt dynamics for the examined glass systems unequivocally encode the nature of the glass topological phases.