The role of disorder and particularly of the interfacial region between crystalline and amorphous phases of indium oxide in the formation of hydrogen defects with covalent (In-OH) or ionic (In-H-In) bonding are investigated using ab initio molecular dynamics and hybrid density-functional approaches. The results reveal that disorder stabilizes In-H-In defects even in the stoichiometric amorphous oxide and also promotes the formation of deep electron traps adjacent to In-OH defects. Furthermore, below-room-temperature fluctuations help switch interfacial In-H-In into In-OH, creating a new deep state in the process. This H-defect transformation limits not only the number of free carriers but also the grain size, as observed experimentally in heavily H-doped sputtered In2Ox. On the other hand, the presence of In-OH helps break O2 defects, abundant in the disordered indium oxide, and thus contributes to faster crystallization rates. The divergent electronic properties of the ionic vs covalent H defects passivation of undercoordinated In atoms vs creation of new deep electron traps, respectively and the different behavior of the two types of H defects during crystallization suggest that the resulting macroscopic properties of H-doped indium oxide are governed by the relative concentrations of the In-H-In and In-OH defects. The microscopic understanding of the H defect formation and properties developed in this work serves as a foundation for future research efforts to find ways to control H species during deposition.