Training VideoLLMs for complex reasoning remains challenging due to sparse sequence level rewards and the lack of fine grained credit assignment over long, temporally grounded reasoning trajectories. While reinforcement learning with verifiable rewards (RLVR) provides reliable supervision, it fails to capture token level contributions, leading to inefficient learning. Conversely, existing self distillation methods offer dense supervision but lack structure and diagnostic specificity, and often interact unstably with reinforcement learning. In this work, we propose VISD, a structured self distillation framework that introduces diagnostically meaningful privileged information for video reasoning. VISD employs a video aware judge model to decompose reasoning quality into multiple dimensions, including answer correctness, logical consistency, and spatio-temporal grounding, and uses this structured feedback to guide a teacher policy for token level supervision. To stably integrate dense supervision with RL, we introduce a direction magnitude decoupling mechanism, where rollout level advantages computed from rewards determine update direction, while structured privileged signals modulate token level update magnitudes. This design enables semantically aligned and fine grained credit assignment, improving both reasoning faithfulness and training efficiency. Additionally, VISD incorporates curriculum scheduling and EMA based teacher stabilization to support robust optimization over long video sequences. Experiments on diverse benchmarks show that VISD consistently outperforms strong baselines, improving answer accuracy and spatio temporal grounding quality. Notably, VISD reaches these gains with nearly 2x faster convergence in optimization steps, highlighting the effectiveness of structured self supervision in improving both performance and sample efficiency for VideoLLMs.