Supervised fine-tuning (SFT) is a prevailing method for adapting large language models to reasoning tasks by imitating offline expert demonstrations, often treating a single expert trajectory as the target behavior. However, reasoning is not simple path imitation: rigidly following one demonstrated solution may overfit to surface forms and suppress the model's own reasoning distribution. We propose Rollout-Adaptive Supervised Fine-Tuning (RASFT), a policy-aware SFT framework that calibrates expert supervision according to problem-level solvability estimated from verified on-policy rollouts. For each problem, RASFT strengthens expert guidance when the current policy struggles, while relaxing rigid imitation and incorporating correct self-generated trajectories when the model already exhibits reliable reasoning behavior. To preserve useful reasoning priors, RASFT further introduces a clipped inverse ratio between the frozen reference model and the current policy to constrain excessive policy drift. Experiments across multiple models on six mathematical reasoning benchmarks and two code reasoning benchmarks show that RASFT achieves better overall performance than SFT, SFT variants, and representative RL methods. The code is available at https://github.com/zjd1sq/RASFT.