Volcanic reservoirs are important fields for oil and gas exploration in China. Affected by multiple volcanic activities and complex diagenesis and tectonic processes, these reservoirs exhibit diverse lithology, well-developed fractures, and strong micro-heterogeneity, which restrict the understanding of such reservoirs. Clearly defining the reservoir characteristics under dual-media conditions is of great guiding significance for the evaluation of storage capacity, optimization of development strategies, and identification of sweet spots in volcanic rock oil reservoirs. To address these challenges, this paper proposes a quantitative classification and evaluation approach for dual-media reservoirs constrained by productivity. Firstly, based on the pore structure characteristic parameters obtained from mercury injection tests (mean pore radius, sorting coefficient, skewness, kurtosis, and coefficient of variation), the K-means clustering method is employed to establish the classification criteria for the matrix, then the Shapley value is incorporated to improve the interpretability of the classification results. Secondly, fracture classification criteria are established using the K-means clustering method based on fracture density derived from electrical micro-imaging (EMI) logs. Finally, by integrating the fracture and matrix classification results, we employ the particle swarm optimization algorithm to optimize the dual-media reservoir classification criteria. The optimization objective is to minimize the total sum of squared deviations of maximum monthly production among different reservoir types within the study area. The classification results are further validated through production characteristic analysis of different reservoir types based on Arps production decline model. The results show that four types of reservoirs with gradually deteriorating physical properties, namely, micro-fracture type, condensed tuff type/tuffaceous sandstone type, tuff type, and tight matrix type, are mainly developed in the study area. The factors influencing the matrix reservoir classification results are, in descending order of significance: permeability, mean pore radius, skewness, and porosity. The fractured reservoirs are classified into four categories based on fracture density thresholds of 11.35, 6.14, and 3.03 fractures/m. Comprehensive classification results reveal that both seepage capacity and storage capacity significantly impact reservoir performance. The Pearson correlation coefficient between the fracture category and comprehensive category is 0.63, while that between the matrix category and comprehensive category is 0.69. Production analysis demonstrates that all wells follow Arps’ exponential decline model, showing a positive correlation between initial production and decline rates. As reservoir quality declines, oil wells exhibit both lower initial production and slower decline rates. This paper not only provides a quantitative understanding of the classification of volcanic rock reservoirs but also offers a methodological reference for characterizing other dual- and triple-media reservoirs requiring multi-dimensional evaluation approaches.