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Ambient pressure X-ray photoelectron spectroscopy is employed to study in real time the chemical reactions occurring on (Ag,Cu)(In,Ga)Se₂ (ACIGSe) surfaces during the first atomic layer deposition (ALD) cycle of HfO_x under realistic synthesis conditions by using tetrakisdimethylamido-hafnium (TDMA-Hf) and H₂O precursors. We find that the initial deposition due to surface reactions of HfO_x ALD on ACIGSe depends on the pretreatment of the ACIGSe surface. While the growth of HfO_x occurs directly upon exposure to the metal precursor for the nontreated (i.e., as-deposited) ACIGSe surface through chemical reactions, the growth is slower for the ACIGSe surface pretreated by postdeposition treatment by RbF. In the latter case, the diffusion of alkali and fluorine elements at the surface is observed during the ALD growth, thus leaving less reactive sites for the TDMA-Hf molecules to adsorb on. The results indicate that an optimization of the ALD of HfO_x on ACIGSe needs to be taken into consideration for alkali metal fluoride-treated ACIGSe.