Precipitation nowcasting, which aims to provide high spatio-temporal resolution precipitation forecasts by leveraging current radar observations, is a core task in regional weather forecasting. Recently, the cascaded architecture has emerged as the mainstream paradigm for deep learning-based precipitation nowcasting. This paradigm involves a deterministic model to predict posterior mean, followed by a probabilistic model to generate local stochasticity. However, existing methods commonly overlook the conflation of the systematic distribution shift in deterministic predictions and the local stochasticity. As a result, the distribution shift of the deterministic component contaminates the predictions of the probabilistic component, leading to inaccuracies in precipitation patterns and intensity, particularly over longer lead times. To address this issue, we introduce RectiCast, a two-stage framework that explicitly decouples the rectification of mean-field shift from the generation of local stochasticity via a dual Flow Matching model. In the first stage, a deterministic model generates the posterior mean. In the second stage, we introduce a Rectifier to explicitly learn the distribution shift and produce a rectified mean. Subsequently, a Generator focuses on modeling the local stochasticity conditioned on the rectified mean. Experiments on two radar datasets demonstrate that RectiCast achieves significant performance improvements over existing state-of-the-art methods.