Multi-agent reinforcement learning (MARL) excels in cooperative and competitive tasks, but most architectures are tied to fixed input-output sizes and require retraining when the number of perceptible or controllable objects changes. While structural generalization techniques mitigate this, they rely on centralized training, raising concerns about scalability and privacy. We propose ADAPT, the first framework to support structural generalization under a decentralized training and decentralized execution (DTDE) paradigm. Every agent adopts an object-centric view, encoding each observed object into a feature vector and aggregating them into a variable-length set representation. To enable each agent to infer task-level contexts from this dynamic input independently, we propose a dynamic-consistency loss that enforces spatio-temporal alignment between context representations and observed environmental dynamics. Agents then condition their policies on the inferred contexts to make locally aligned decisions. For zero-shot transfer, we propose FINE (Foresight INdex for multi-agEnt), a metric that considers Q-value overestimation and enables cross-policy comparison of long-term impact, facilitating effective policy transfer. Experiments show that ADAPT surpasses existing DTDE methods and outperforms CTDE baselines in zero-shot generalization.