Massive MIMO systems can enhance spectral and energy efficiency, but they require accurate channel state information (CSI), which becomes costly as the number of antennas increases. While machine learning (ML) autoencoders show promise for CSI reconstruction and reducing feedback overhead, they introduce new challenges with standardization, interoperability, and backward compatibility. Also, the significant data collection needed for training makes real-world deployment difficult. To overcome these drawbacks, we propose an ML-based, decoder-only solution for compressed CSI. Our approach uses a standardized encoder for CSI compression on the user side and a site-specific generative decoder at the base station to refine the compressed CSI using environmental knowledge. We introduce two training schemes for the generative decoder: An end-to-end method and a two-stage method, both utilizing a goal-oriented loss function. Furthermore, we reduce the data collection overhead by using a site-specific digital twin to generate synthetic CSI data for training. Our simulations highlight the effectiveness of this solution across various feedback overhead regimes.