One of the primary objectives of satellite remote sensing is to capture the complex dynamics of the Earth environment, which encompasses tasks such as reconstructing continuous cloud-free image sequences, detecting land cover changes, and forecasting future surface evolution. However, existing methods typically require specialized models tailored to different tasks, and lack a general framework that can address these multi-level tasks from a unified perspective. In this paper, we propose a Unified Spatio-Temporal Generative Model (UniTS), which integrates several long-separated core tasks, including time series reconstruction, time series cloud removal, time series semantic change detection, and time series forecasting. Based on the flow matching generative paradigm, UniTS constructs a deterministic evolution path from noise to targets under the guidance of task-specific conditions, achieving unified modeling of spatiotemporal representations for multi-level tasks. The UniTS architecture consists of a diffusion transformer with spatiotemporal blocks, where we design an Adaptive Condition Injector (ACor) to enhance the model's conditional perception of multimodal inputs, enabling high-quality controllable generation. Additionally, we design a Spatiotemporal-aware Modulator (STM) to improve the ability of spatiotemporal blocks to capture complex spatiotemporal dependencies. It substantially outperforms existing specialized models, particularly under challenging conditions such as severe cloud contamination, modality absence, and forecasting complex phenological variations.