This study aimed to address the poor structural stability and limited carbon pool expansion of soda saline–alkali soil by conducting a 180-day laboratory incubation experiment. Four treatments were established, including a control (CK), natural humus material alone (HM), and natural humus material combined with iron oxide (HMFe) or aluminum oxide (HMAl). Soil water-stable aggregate distribution, CO₂ emissions, and physicochemical properties were determined, and a first-order kinetic model was applied to elucidate the driving mechanisms of soil physical structure and biogeochemical processes under different amendments. The results showed that: (1) Compared with CK, the HM treatment exhibited the strongest enhancement of macroaggregate formation and stability, with macroaggregate content increasing by 21.83%. Although the combined application of natural humus with iron/aluminum oxides significantly increased soil organic carbon (SOC) content, competitive adsorption on mineral surfaces interfered with the physical cementation of organic matter, resulting in a lower mean weight diameter than that under the HM treatment. (2) All amended treatments induced a positive priming effect on organic carbon mineralization. Among them, the HMAl treatment exhibited the highest mineralization rate constant (0.0091 d^_-1), primarily due to alleviation of alkaline stress through a significant reduction in soil pH; however, owing to strong chemical protection, it showed the lowest potentially mineralizable carbon pool and cumulative CO₂ emissions. (3) Aggregate stability was significantly and positively correlated with cumulative CO₂ emissions, indicating that microbially driven aggregate formation was accompanied by carbon consumption. Overall, natural humus primarily promoted physical aggregation by stimulating microbial activity, whereas the addition of iron/aluminum oxides partially hindered macroaggregate formation and accelerated labile carbon turnover but enhanced SOC retention through chemical stabilization. Therefore, soil amelioration strategies for soda saline–alkali soils should comprehensively balance physical structural stability and chemical carbon sequestration capacity.