Climate change and human activities have a great impact on the environment and have challenged the assumption of the stability of the hydrological time series and the consistency of the observed data. In order to investigate the applicability of machine learning (ML)-based rainfall–runoff (RR) simulation methods under a changing environment scenario, several ML-based RR simulation models implemented in novel continuous and non-real-time correction manners were constructed. The proposed models incorporated categorical boosting (CatBoost), a multi-hidden-layer BP neural network (MBP), and a long short-term memory neural network (LSTM) as the input–output simulators. This study focused on the Dongwan catchment of the Yiluo River Basin to carry out daily RR simulations for the purpose of verifying the model’s applicability. Model performances were evaluated based on statistical indicators such as the deterministic coefficient, peak flow error, and runoff depth error. The research findings indicated that (1) ML-based RR simulation by using a consistency-disrupted dataset exhibited significant bias. During the validation phase for the three models, the R2 index decreased to around 0.6, and the peak flow error increased to over 20%. (2) Identifying data consistency transition points through data analysis and conducting staged RR simulations before and after the transition point can improve simulation accuracy. The R2 values for all three models during both the baseline and change periods were above 0.85, with peak flow and runoff depth errors of less than 20%. Among them, the CatBoost model demonstrated superior phased simulation accuracy and smoother simulation processes and closely matched the measured runoff processes across high, medium, and low water levels, with daily runoff simulation results surpassing those of the BP neural network and LSTM models. (3) When simulating the entire dataset without staged treatment, it is impossible to achieve good simulation results by adopting uniform extraction of the training samples. Under this scenario, the MBP exhibited the strongest generalization capability, highest prediction accuracy, better algorithm stability, and superior simulation accuracy compared to the CatBoost and LSTM simulators. This study offers new ideas and methods for enhancing the runoff simulation capabilities of machine learning models in changing environments.