Dynamics of red-ox reactions occurring over catalysts with active oxide support is described by mathematical modeling. Numerical analysis is applied to transients from an initially oxidized state of a Pt/PrCeZrO catalyst to a partially reduced steady state present during CH4 dry reforming. Oxygen transport to the surface from adjacent regions in the catalyst lattice is considered to quantify the impact on the transient behavior in the model red-ox reaction over the catalyst with a high lattice oxygen mobility. Chemical transformations and coverages at the catalyst surface are largely affected by the internal transport of oxygen species, while the overall character and shape of transient curves remain defined by the specificity of the reaction kinetic scheme. Detailed analysis of CH4 dry reforming over a Pt/PrCeZrO catalyst at contact times of 4.7, 8, and 15 ms allowed to (1) clarify the factors that control dynamic system behavior and catalytic properties, (2) discriminate kinetic schemes, (3) confirm a high efficiency of cationic Pt species in CH4 dissociation, and (4) underpin that CO2 transformation may occur via carbonate intermediates located on oxidized Ptn+−-Pr4+-O surface sites. Direct estimation of bulk oxygen diffusion rate as well as kinetic parameters was carried out. Findings are consistent with the characteristics of the catalyst surface state and oxygen mobility in the surface/bulk layers.