Unsupervised domain adaptation (UDA) has emerged as a promising approach to address domain shifts in remote-sensing scene classification. The acquisition of labelled data from diverse geographic, temporal, and sensor domains often presents significant challenges, rendering the UDA an essential tool for real-world applications. Traditional UDA methodologies typically focus on single-source domains. However, real-world scenarios frequently involve multi-source domains with diverse distributions, which introduce additional challenges such as inter-source discrepancy, label noise, class imbalance and explainability. To address these challenges, an explainable multi-source UDA framework is proposed which integrates feature extraction through contrastive-learning with an adaptive clustering-based pseudo-labeling named as XMUDA-CLAC. The pseudo-label generation process is further refined through a multi-objective optimization approach. To enhance transparency and interpretability, Explainable Artificial Intelligence (XAI) methodologies are employed to visualize the attention maps generated by contrastive learning-based Vision Transformer (ViT). The proposed XMUDA-CLAC framework is assessed using four benchmark remote sensing datasets—AID (A), NWPU-RESISC45 (N), PatternNet (P), and UC Merced (U)—under various domain-shift scenarios: (A → U), (P → N), (U → P), (A, P → U), (A, N → U), (P, U → N), (A, P, N → U), and (A, U, P → N). In this context, the proposed method demonstrates absolute accuracy improvements of 0.62%, 0.94%, 0.73%, 0.41%, 0.51%, 1.66%, 0.20%, and 0.10% over the best-performing baselines, respectively. This illustrates the efficacy of the framework in scenarios involving multi-source domain adaptation with better interpretability. The source code is available at https://github.com/BinuJoseA/XMUDA-CLAC.