It's important not to mix up terms here. What you get after combustion are oxides: Na2O, CaO, K2O, MgO, etc (probably some superoxides as well, but I digress). These are not oxidants, because the metals are in very stable oxidation states. But they are very reactive towards water: the oxide anions "steal" protons from water, giving hydroxide ions as product. Specifically, in the case of K2O, the reaction would be something like: K2O + H2O ➡️2K+ + 2OH-. The hydroxide ions then react with triglycerides in the saponification reaction.