Asynchronous decentralized federated learning (ADFL) eliminates central coordination and global synchronization, making it attractive for large-scale and heterogeneous systems. However, frequent peer-to-peer communication, asynchronous updates on directed topologies, and non-IID data jointly lead to excessive communication overhead, biased aggregation and severe model drift. We propose PushCen-ADFL, a communication-efficient ADFL framework that enables stable training under asymmetric communication and delayed client participation. PushCen-ADFL couples communication, aggregation, and local stabilization in a shared centroid representation space, forming a closed loop between compression and optimization. Clients exchange centroid-form messages, apply average-preserving push-sum mixing to correct aggregation bias, and use a lightweight centroid regularization anchored in the same centroid space to mitigate drift under heterogeneity and staleness. A bounded, sender-deduplicated buffer further improves robustness under irregular asynchronous arrivals. Experiments on vision datasets demonstrate that PushCen-ADFL improves accuracy under data heterogeneity by up to 6\% while reducing per-push communication cost by more than 80\%, achieving a favorable accuracy-communication trade-off.