Deep learning-based just-in-time soft sensors effectively handle the strong nonlinearity of complex process industry, but their implementation faces significant challenges in interpretability and time cost. Hence, a just-in-time soft sensor based on spatiotemporal graph decoupling is proposed. To decrease time cost, it employs a global-local modeling strategy: pre-training on all historical data to build a global model, and fine-tuning with relevant samples to deliver a local model. To enhance interpretability, couplings that reflect how variables interact with each other in spatiotemporal dimensions are constructed, conforming to prior knowledge, to guide the graph neural network as a global model during pre-training. The global model decouples variables to quantify their influence as intrinsic information, enabling a clearer understanding of how each variable contributes to the prediction. Following the intrinsic information, relevant samples are then selected with the preset relevance metric to fine-tune the global model. Finally, two industrial cases demonstrate this model's low runtime, effectiveness, and physical consistency from the perspectives of underlying physics.