Subtle volcanic deformations point to volcanic activities, and monitoring them helps predict eruptions. Today, it is possible to remotely detect volcanic deformation in mm/year scale thanks to advances in interferometric Synthetic Aperture Radar (InSAR). This paper proposes a framework based on a deep learning model to automatically discriminate subtle volcanic deformations from other deformation types in five-year-long InSAR stacks. Models are trained on a synthetic training set. To better understand and improve the models, explainable AI analyses are performed. In initial models, gradient-weighted Class Activation Mapping (Grad-CAM) linked new-found patterns of slope processes and salt lake deformations to falsepositive detections. The models are then improved by fine-tuning with a hybrid synthetic-real data, and additional performance is extracted by low-pass spatial filtering of the real test set. T-SNE latent feature visualization confirmed the similarity and shortcomings of the fine-tuning set, highlighting the problem of elevation components in residual tropospheric noise. After fine-tuning, all the volcanic deformations are detected, including the smallest one, Lazufre, deforming 5 mm/year. The first time confirmed deformation of Cerro El Condor is observed, deforming 9.9-17.5 mm/year. Finally, sensitivity analysis uncovered the model's minimal detectable deformation of 2 mm/year.