Domains of cocontinuous polymer blends coarsen during annealing. In general, coarsening undergoes two regimes: linear growth followed by slower nonlinear growth. While the linear regime is well understood by several theories, the number of studies on the nonlinear regime is scarce and often inconclusive. Herein, we examine the entire spectrum of the coarsening of cocontinuous polymer blends using an in situ high-temperature confocal rheology technique. By linking 4-dimensional microscopic details (time evolution of three-dimensional microscopic details) with the rheological properties, we demonstrate that the transition to the nonlinear regime is associated with the onset of droplet formation during the coarsening of these blends. Such transitions and morphological changes occurred only in the blends with high interfacial tension to zero-shear viscosity ratio (Gamma/eta(0)). This phenomenon provides a framework for comprehensive model development. By analyzing the data from the literature, we propose that there exists a critical Gamma/eta(0) ratio beyond which the system undergoes such transitions.