Abstract: Secure transmission of electrocardiogram (ECG) signals remains a major challenge in telecardiology. While traditional mathematical watermarking can embed patient metadata directly into ECG signals, it is highly fragile against temporal desynchronization such as circular phase shifts. In contrast, existing deep watermarking approaches for temporal signals, such as audio, typically rely on lossy quantization, which compromises the high-frequency micro-morphological details critical for clinical diagnosis. To bridge this gap, we propose ECGWmark, a fully convolutional and quantization-free deep watermarking framework for medical time-series. ECGWmark operates in a continuous, full-resolution latent space and utilizes a localized frame-level mechanism to improve the robustness to severe desynchronization. Crucially, we introduce a differentiable Physiological Loss guided by a clinical classifier to preserve diagnostic semantics. Experiments on the benchmark MIT-BIH database show that ECGWmark maintains channel-bit extraction accuracy above 90% under the evaluated circular temporal shifts. Furthermore, under a rigorous inter-patient diagnostic evaluation, Class-V sensitivity changes from 71.97% to 76.50%, whereas Macro-F1 changes from 35.25% to 34.71% and Class-S sensitivity from 8.89% to 1.39%; these results indicate mixed class-level effects.