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In this work, the hydrogenation mechanism of fired passivating contacts (FPC) based on c-Si/SiO$_{x}$/nc-SiC$_{x}$(p) stacks was investigated, by correlating the passivation and local re-distribution of hydrogen. Secondary ion mass spectroscopy (SIMS) depth profiling was used to assess the hydrogen (/deuterium) content. The SIMS profiles show that hydrogen almost completely effuses out of the SiC$_{x}$(p) during firing, but can be re-introduced by hydrogenation via forming gas anneal (FGA) or by release from a hydrogen containing layer such as SiN$_{x}$:H. A pile-up of H at the c-Si/SiO$_{x}$ interface was observed and identified as a key element in the FPC's passivation mechanism. Moreover, the samples hydrogenated with SiN$_{x}$:H exhibited higher H content compared to those treated by FGA, resulting in higher iV$_{OC}$ values. Further investigations revealed that the doping of the SiC$_{x}$ layer does not affect the amount of interfacial defects passivated by the hydrogenation process presented in this work. Eventually, an effect of the oxide's nature on passivation quality is evidenced. iV$_{OC}$ values of up to 706 mV and 720 mV were reached with FPC test structures using chemical and UV-O$_{3}$ tunneling oxides, respectively, and up to 739 mV using a reference passivation sample featuring a ~25 nm thick thermal oxide., Comment: 13 pages, 5 figures