Resting-state functional magnetic resonance imaging (rs-fMRI) and its derived functional connectivity networks (FCNs) have become critical for understanding neurological disorders. However, collaborative analyses and the generalizability of models still face significant challenges due to privacy regulations and the non-IID (non-independent and identically distributed) property of multiple data sources. To mitigate these difficulties, we propose Domain Adversarial Federated Learning (DAFed), a novel federated deep learning framework specifically designed for non-IID fMRI data analysis in multi-site settings. DAFed addresses these challenges through feature disentanglement, decomposing the latent feature space into domain-invariant and domain-specific components, to ensure robust global learning while preserving local data specificity. Furthermore, adversarial training facilitates effective knowledge transfer between labeled and unlabeled datasets, while a contrastive learning module enhances the global representation of domain-invariant features. We evaluated DAFed on the diagnosis of ASD and further validated its generalizability in the classification of AD, demonstrating its superior classification accuracy compared to state-of-the-art methods. Additionally, an enhanced Score-CAM module identifies key brain regions and functional connectivity significantly associated with ASD and MCI, respectively, uncovering shared neurobiological patterns across sites. These findings highlight the potential of DAFed to advance multi-site collaborative research in neuroimaging while protecting data confidentiality.