LLMs can personalize education, although current static-prompt tutoring systems struggle to adapt to diverse academic disciplines. We develop and test a system with subject-aware prompting, based on 14 pedagogical features (e.g., tutor scaffolding, student understanding) extracted from raw transcripts. We first train a prompt routing model in a simulation environment, and then deploy it for online adaptation with actual high-school students. The simulation benchmark shows the router outperforming two static baselines (0.694 vs. 0.647 and 0.64, p<0.001). A/B testing (N=656 conversations from 359 students) shows sim-to-real transfer where the model switches from analytical to scaffolding learning strategies. Our adaptive prompt selection mechanism improves instructional efficiency, maintains pedagogical quality and reduces interactions by around 3 turns (p=0.007). While a greedy router achieves a comparable exercise conversion rate with the baseline (19.1% vs. 19.6%), a stochastic router that samples strategies leads to a higher conversion rate (28.1%).