Continuous cardiac monitoring during sleep is vital for detecting silent arrhythmia and other nocturnal cardiac events. While electrocardiogram (ECG) is the clinical gold standard, its reliance on electrodes and physical contact makes it intrusive for daily long-term use. Millimeter-wave (mmWave) radar offers a compelling non-contact alternative by capturing cardiac-induced chest-wall micro-vibrations. Existing radar-to-ECG methods often rely on direct waveform regression, assuming posture-stable mappings that break under natural sleep movements and obscure true cardiac rhythms. Inspired by the modality-invariant perception observed in speech and vision, we introduce mmJEPA-ECG, a physiology-guided framework for reconstructing clinical ECGs by anchoring radar sensing to invariant cardiac dynamics. It addresses two fundamental challenges: (i) disentangling robust cardiac representations from posture-induced artifacts, and (ii) generalizing ECG reconstruction across individuals under signal ambiguity. To address these challenges, Physiology-Oriented Self-Supervised Pretraining builds on a Joint Embedding Predictive Architecture (JEPA) with domain-informed masking and heart rate consistency to extract posture-robust cardiac embeddings. Conditional Diffusion-based ECG Reconstruction then generates personalized ECG waveforms through a hierarchical conditional diffusion process by spectral fidelity and denoising constraints. Extensive experiments on both public and self-collected multi-subject datasets demonstrate that our method outperforms state-of-the-art across waveform and rhythm metrics, halving R-R peak errors even under posture shifts and arrhythmic conditions. Codes and dataset are released at https://github.com/lanyangyang/mmJEPA-ECG.