Organic aerosols (OA) in the atmosphere are composed of molecules with highly diverse chemical structures and functionalities. The OH-initiated heterogeneous aging of these organic molecules could occur in multiple generations, exponentially increasing the complexity of the oxidation products. Furthermore, the detailed reaction mechanisms are likely different and site-specific as the OA's chemical structures vary. To systematically study these mechanisms, in this work, heterogeneous OH oxidation of five surrogate diacid OA with different positions and numbers of branched methyl groups was examined in a flow tube reactor. The oxidation products were characterized by an ion mobility mass spectrometer, which could resolve isomers and unambiguously identify individual products. Through detailed analysis of the molecular compositions of the oxidized OA, we suggest that the site-specific oxidation mechanisms largely modulate the oxidation products from the functionalization, fragmentation, and oligomerization pathways. Depending on the molecular structures and adjacent functional group(s), oxidation on primary carbons could play a key role, while that on secondary and tertiary carbons could be less important if hindered by the mesomeric effect. Our results also suggest that fragmentation products are most likely formed from later-generation reactions, while functionalization occurs only at certain carbon sites in later generations. Finally, oligomers are also largely affected by the molecular structures of the parent OA, evidenced by the distinct carbon oxidation state patterns and distributions across carbon numbers. This work provides new insights into the detailed reaction mechanisms from heterogeneous OH oxidation for diverse organic molecules.