Precipitation nowcasting is vital for flood warning, agricultural management, and emergency response, yet two bottlenecks persist: the prohibitive cost of modeling million-scale spatiotemporal tokens from multi-variate atmospheric fields, and the extreme long-tailed rainfall distribution where heavy-to-torrential events -- those of greatest societal impact -- constitute fewer than 0.1% of all samples. We propose the Precipitation-Adaptive Network (PA-Net), a Transformer framework whose computational budget is explicitly governed by rainfall intensity. Its core component, Precipitation-Adaptive MoE (PA-MoE), dynamically scales the number of activated experts per token according to local precipitation magnitude, channeling richer representational capacity toward the rare yet critical heavy-rainfall tail. A Dual-Axis Compressed Latent Attention mechanism factorizes spatiotemporal attention with convolutional reduction to manage massive context lengths, while an intensity-aware training protocol progressively amplifies learning signals from extreme-rainfall samples. Experiment on ERA5 demonstrate consistent improvements over state-of-the-art baselines, with particularly significant gains in heavy-rain and rainstorm regimes.