Longitudinal passive sensing enables continuous health prediction, yet models often fail under cross-dataset distribution shifts. Traditional ML overfits cohort-specific artifacts, while Large Language Models (LLMs) struggle to reason reliably over long, heterogeneous time-series. We introduce TimeSRL, a two-stage LLM framework that routes predictions through an explicit semantic bottleneck. The model first abstracts raw signals into high-level natural language, then predicts behavioral outcomes from these abstractions alone. This forces the model to reason over semantic concepts that we argue generalize better than raw numbers. We optimize this process end-to-end using Group Relative Policy Optimization (GRPO) with Reinforcement Learning from Verifiable Rewards (RLVR), learning outcome-aligned abstractions without gold intermediate annotations. Instantiated on mental-health prediction, TimeSRL achieves state-of-the-art performance on a benchmark designed to stress-test cross-cohort generalization under a rigorous leave-one-dataset-out (LOSO) protocol, reducing mean absolute error (MAE) over strong non-LLM ML and LLM baselines by 3.1--10.1% and 9.5--44.1% for anxiety, and 3.2--9.6% and 27.4--57.6% for depression (all $p$s<0.05). TimeSRL significantly outperforms prior methods in cross-benchmark transfer across different sensing pipelines, rivaling its own within-domain performance without target-domain fine-tuning. These results demonstrate that semantic abstractions are reusable and point to a new direction for generalizable behavior modeling via RL-tuned LLMs.