Experience-based self-evolution is crucial for LLM agents, but existing benchmarks often assume explicit goals, stable task patterns, and clear feedback. We study a more challenging setting: low-repetition tasks with implicit rewards, where past experience is difficult to reuse and feedback is delayed, noisy, and outcome-level. We introduce \textsc{FinEvolveBench}, a temporally controlled benchmark for financial sentiment prediction that links daily news-driven predictions to future excess returns. We further propose Tree-of-Experience (ToE), a structured experience-management method that organizes, retrieves, validates, and updates agent experience. Experiments show that general-purpose experience mechanisms do not consistently outperform no-experience baselines, while ToE achieves stronger overall performance. These results highlight the importance of structured experience management for self-evolving agents in implicit-reward environments.