Deep Learning (DL)-based channel state information (CSI) feedback is a promising technique for the transmitter to accurately acquire the CSI of massive multiple-input multiple-output (MIMO) systems. As critical concerns about DL-based physical layer applications, the intra-domain generalizability affected by dataset bias and inter-domain robustness in data drift remain challenging. Therefore, we build on a Hybrid Complex-Valued Lightweight framework, namely the HybridCVLNet, capable of overcoming the dataset bias with regularized hybrid structure and codeword. Meanwhile, a corresponding transductive-based hybrid domain adaptation scheme is proposed to tackle the inter-domain data drift. The experiment verifies that HybridCVLNet achieves stable generalizability and performance gain over the state-of-the-art (SOTA) feedback schemes in an intra-domain heterogeneous dataset. In addition, its transductive-based hybrid domain adaptation scheme is more efficient and superior to the inductive-based transfer learning methods under two inter-domain online re-optimization settings.