Digital watermarking secures electroencephalogram (EEG) data in distributed Brain–Computer Interface (BCI) environments. However, existing single-domain deep learning schemes struggle to maintain robustness against clinical signal processing attacks due to EEG’s joint time–frequency nature. We introduce the Dual-Stream Frequency–Time Attention Network (DS-FTAN), utilizing an adaptive Spectral Gating Mechanism to embed information within robust, high-energy EEG spectral regions. A robustness simulation layer—encompassing resampling, spectral dropout, and band-pass filtering—is incorporated during training. Validations confirm DS-FTAN balances imperceptibility (PSNR > 36 dB) with reliable recovery. Specifically, it achieves >99.99% accuracy under no-attack conditions and maintains 86.52–98.77% accuracy across complex attacks (e.g., 50% cropping, band-pass filtering). This significantly outperforms time-domain baselines. Furthermore, DS-FTAN exhibits excellent zero-shot cross-channel generalization. It preserves diagnostic integrity, causing merely a 0.42% accuracy drop in downstream EEGNet intention recognition. Ultimately, this framework provides a reliable solution for privacy-preserving EEG data sharing.