The response of lipid bilayers to osmotic stress is an important part of cellular function. Previously, in [Oglecka et al. 2014], we reported that cell-sized giant unilamellar vesicles (GUVs) exposed to hypotonic media, respond to the osmotic assault by undergoing a cyclical sequence of swelling and bursting events, coupled to the membrane's compositional degrees of freedom. Here, we seek to deepen our quantitative understanding of the essential pulsatile behavior of GUVs under hypotonic conditions, by advancing a comprehensive theoretical model for vesicle dynamics. The model quantitatively captures our experimentally measured swell-burst parameters for single-component GUVs, and reveals that thermal fluctuations enable rate dependent pore nucleation, driving the dynamics of the swell-burst cycles. We further identify new scaling relationships between the pulsatile dynamics and GUV properties. Our findings provide a fundamental framework that has the potential to guide future investigations on the non-equilibrium dynamics of vesicles under osmotic stress.