Due to the wide distribution of construction sites and data heterogeneity, single site models struggle with cross-site generalization and privacy compliance. A collaborative prediction model is needed to integrate information from multiple sites and enhance governance. Traditional time series models fail to capture short-term disturbances and long-term dependencies, and construction site data often includes abrupt changes and multi-scale dynamics. Non-Independent and Identically Distributed (Non-IID) data and sample imbalance across sites can lead to client drift, reducing model generalization. To address these challenges, this paper proposes a parallel multi-site dust prediction framework combining the improved hybrid model DustLSTM-Trans and the federated learning mechanism FedProx-Dyn, enabling knowledge sharing without aggregating raw data. This framework improves model collaboration while ensuring prediction accuracy and timeliness. Evaluations with data from multiple construction sites show that the framework reduces prediction errors between sites and enhances cross-site generalization. Compared to traditional models, The performance of DustLSTM-Trans is improved by 22.7 %, 26.2 % and 8.2 % on RMSE, MSE and R 2, respectively, while FedProx-Dyn shows 31.6 % performance boost. The overall framework supports real-time learning and adaptive parameter updates across construction sites while ensuring data transmission efficiency and privacy preservation. The model provides accurate dust pollution warnings in different environments and could be adapted to other pollution scenarios, such as road dust and industrial emissions.