Deep learning-based cardiac MRI reconstruction faces significant domain shift challenges when deployed across multiple clinical centers with heterogeneous scanner configurations and imaging protocols. We propose HierAdaptMR, a hierarchical feature adaptation framework that addresses multi-level domain variations through parameter-efficient adapters. Our method employs Protocol-Level Adapters for sequence-specific characteristics and Center-Level Adapters for scanner-dependent variations, built upon a variational unrolling backbone. A Universal Adapter enables generalization to entirely unseen centers through stochastic training that learns center-invariant adaptations. The framework utilizes multi-scale SSIM loss with frequency domain enhancement and contrast-adaptive weighting for robust optimization. Comprehensive evaluation on the CMRxRecon2025 dataset spanning 5+ centers, 10+ scanners, and 9 modalities demonstrates superior cross-center generalization while maintaining reconstruction quality.