The anomalous Hall effect (AHE) reported in epitaxial RuO2/TiO2 has been attributed to a strain-stabilized magnetic state, but strain can be entangled with Ru-Ti intermixing and interfacial charge redistribution, which can produce Ti3+ and potentially localized moments. Here, we disentangle these contributions using Ti-alloyed RuO2 heterostructures in which abundant Ti3+ states are retained while epitaxial strain is independently changed. The strained and relaxed films have nearly identical Ti/Ru compositions and comparable Ti3+ fractions, yet a pronounced nonlinear AHE appears only in the coherently strained film, while the relaxed heterostructure exhibits an almost linear Hall response. Spectroscopic ellipsometry further shows that the AHE-active strained state is accompanied by a reconstruction of the itinerant electronic response, including enhanced metallicity and longer carrier relaxation times. These results show that Ti3+ formation alone is insufficient to generate the anomalous Hall state and identify epitaxial strain, through its modification of the itinerant RuO2 electronic structure, as the dominant control parameter.