Warm asphalt mixtures can suffer from decreased short-term high-temperature performance; therefore, introducing additional modifiers can mitigate this risk. This study investigates the effects of a liquid organosilane warm mix additive (WMAd) and grade-bumping polyethylene-based additive added simultaneously to asphalt binders on their chemical composition and its relationship with performance characteristics. Previous studies found relationships between the formation of certain chemical species during bitumen ageing and the increase in their viscosity, stiffness and other performance characteristics—the present work intended to verify these relationships when the two mentioned additives are used. Two asphalt binders were investigated—a paving-grade 50/70 binder and a 45/80-55 polymer-modified bitumen. The chemical analysis was performed using Fourier-transform infrared (FTIR) spectroscopy in attenuated total reflectance mode and focused on the quantification of carbonyl, sulfoxide, polybutadiene and polystyrene structures in the asphalt binders subjected to laboratory short- and long-term ageing. Additionally, the relationships between asphalt binder performance and selected FTIR indices were evaluated using a dynamic shear rheometer. It was found that the investigated additives significantly affected the apparent contents of all evaluated chemical structures in the asphalt binders; however, these changes were not reflected in their performance evaluation.