We report a generic theoretical framework for accurate simulation of the temporal and spatial evolution of fused fiber-optic components, fabricated by the "heat and pull" technique. The methodology is based on the solution of quasi-3D incompressible Navier-Stokes equations formulated for immiscible two-phase flow. The two-phase interface is resolved by employing an interface tracking approach combined with the immersed boundary method. The model facilitates accurate spatiotemporal prediction of the evolution of both the external shape of the optical component and the internal dopant concentration during fabrication. Validation of the model was obtained by extensive comparison to experimental results. The model was found to be a convenient theoretical tool that may reliably facilitate the design and fabrication process of a wide spectrum of optic components.