Due to their eco-sustainability and versatility, organic electrodes are promising candidates for large-scale energy storage in rechargeable aqueous batteries. This is notably the case of aqueous hybrid batteries that pair the low voltage of a zinc anode with the high voltage of a quinone-based (or analogue of quinone-based) organic cathode. However, the mechanisms governing their charge-discharge cycles remain poorly understood and are even a matter of debate and controversy. No consensus exists on the charge carrier in mild aqueous electrolytes, especially when working in an electrolyte containing a multivalent metal cation such as Zn$^{2+}$. In this study, we comprehensively investigate the electrochemical reactivity of two model quinones, chloranil and duroquinone, either diluted in solution or incorporated into carbon-based composite electrodes. We demonstrate that a common nine-member square scheme proton-coupled electron transfer mechanism allows us to fully describe and rationalize their electrochemical behavior in relation to the pH and chemical composition of the aqueous electrolyte. Additionally, we highlight the crucial role played by the pKas associated with the reduced states of quinones in determining the nature of the charge carrier that compensates for the negative charges reversibly injected in the active material. Finally, contrary to the widely reported findings for Zn/organic batteries, we unequivocally establish that the predominant solid-state charge carriers in Zn$^{2+}$-based mild aqueous electrolytes are not multivalent Zn$^{2+}$ cations but rather protons supplied by the weakly acidic hexaaqua metal ions (i.e., [Zn(H$_2$O)$_6$]$^{2+}$]).