Time-series data augmentation plays a crucial role in regression-oriented forecasting tasks, where limited data restricts the performance of deep learning models. While Generative Adversarial Networks (GANs) have shown promise in synthetic time-series generation, existing approaches primarily focus on matching marginal data distributions and often overlook the temporal dynamics that naturally exist in the original multivariate time series. When generating multivariate time series, this mismatch leads to distribution shift and temporal drift, thereby degrading the fidelity of the synthetic sequences. In this work, we propose a model-agnostic Markov Chain Monte Carlo (MCMC)-based framework to mitigate distribution shift and preserve temporal dynamics in synthetic time series. We provide a theoretical analysis of how conditional generative models accumulate deviations under sequential generation and demonstrate that the MCMC algorithm can correct these discrepancies by enforcing consistency with empirical transition statistics between neighboring time points. Extensive experiments on the Lorenz, Licor, ETTh, and ILI datasets using RCGAN, GCWGAN, TimeGAN, SigCWGAN, and AECGAN demonstrate that the proposed MCMC framework consistently improves autocorrelation alignment, skewness error, kurtosis error, R$^2$, discriminative score, and predictive score. These results suggest that synthetic time series consistent with the original data require explicit preservation of transition laws rather than solely relying on adversarial distribution matching, thereby offering a principled direction for improving generative modeling of time-series data.