The molten core method (MCM) is a versatile technique to fabricate a wide variety of optical fiber core compositions ranging from novel glasses to crystalline semiconductors. One common feature of the MCM is an interaction between the molten core and softened glass cladding during the draw process, which often leads to compositional modification between the original preform and the drawn fiber. This causes the final fiber core diameter, core composition, and associated refractive index profile to vary over time and longitudinally along the fiber. Though not always detrimental to performance, these variations must, nonetheless, be anticipated and controlled as they directly impact fiber properties (e.g., numerical aperture, effective area). As an exemplar to better understand the underlying mechanisms, a silica-cladding, YAG-derived yttrium aluminosilicate glass optical fiber was fabricated and its properties (core diameter, silica concentration profile) were monitored as a function of draw time/length. It was found that diffusion-controlled dissolution of silica into the molten core agreed well with the observations. Following this, a set of first order kinetics equations and diffusion equation using Fick's second law was employed as an initial effort to model the evolution of fiber core diameter and compositional profile with time. From these trends, further insights into other compositional systems and control schemes are provided.