Due to their remarkable mechanical and chemical properties, Ti-Al based materials are attracting considerable interest in numerous fields of engineering, such as automotive, aerospace, and defense. With their low density, high strength, and resistance to corrosion and oxidation, these intermetallic alloys and compound metal-metallic composites have found diverse applications. The present study delves into the interfacial dynamics of these Ti-Al systems, particularly focusing on the behavior of Ti and Al atoms in the presence of TiAl$_3$ grain boundaries under experimental heat treatment conditions. Using a combination of Molecular Dynamics and Markov State Model analyses, we scrutinize the kinetic processes involved in the formation of TiAl$_3$. The Molecular Dynamics simulation indicates that at the early stage of heat treatment, the predominating process is the diffusion of Al atoms towards the Ti surface through the TiAl$_3$ grain boundaries. The Markov State Modeling identifies three distinct dynamic states of Al atoms within the Ti/Al mixture that forms during the process, each exhibiting a unique spatial distribution. Using transition timescales as a qualitative measure of the rapidness of the dynamics, it is observed that the Al dynamics is significantly less rapid near the Ti surface compared to the Al surface. Put together, the results offer a comprehensive understanding of the interfacial dynamics and reveals a three-stage diffusion mechanism. The process initiates with the premelting of Al, proceeds with the prevalent diffusion of Al atoms towards the Ti surface, and eventually ceases as the Ti concentration within the mixture progressively increases. The insights gained from this study could contribute significantly to the control and optimization of manufacturing processes for these high-performing Ti-Al based materials.