In this work, the correlation between structure, composition, surface state, and CO oxidation catalytic activity of the ternary oxide Ag2CuMnO4 was studied. The stepwise surface and structure modification was implemented with the use of pretreatments in different media at various temperatures. It allowed investigating the nature of low-temperature catalytic activity and determining the conditions for the realization of the most efficient route of CO oxidation. The investigation of the interaction of the ternary oxide with carbon monoxide was carried out using TPR-CO, in situ XRD, and ex situ XPS methods. Ex situ XPS was applied to study the evolution of composition and charge state of the ternary oxide components on the surface of particles during the interaction with the reaction CO + O2 mixture versus the temperature, preventing the contact of the sample with the air. Ex situ XPS data established the presence of prominent charge transfer between copper and manganese within the delafossite structure during the interaction with CO. The results of catalytic measurements revealed that the most active Ag2CuMnO4 state can be achieved by heating in the inert or in the reaction mixture at 250 °C. Under these conditions, the enhancement of an interlayer charge transfer occurs at the expense of Cu+ ions accumulation in the linear-coordinated cation layer. The heating above 300 °C led to the appearance of tetrahedral Cu+ cations within the "proto-spinel" entities determining the drop in catalytic activity. The data obtained outline the importance of linear and octahedral charge transfer for low-temperature CO oxidation activity.