Self-evolving agents improve through continual self-play and self-generated learning signals, but their internally generated tasks and verifier signals provide limited coverage of phase-level errors, allowing capability degradation and safety drift to accumulate. We introduce ANCHOR, an LLM-based supervisory framework that delivers evaluative feedback at multiple phases of self-evolution and aggregates reviewed signals into context for subsequent steps. We retrofit two representative open-source self-evolving agent frameworks with ANCHOR, and evaluate them across coding, mathematical reasoning, and safety. Our results show that ANCHOR substantially improves safety performance while maintaining stable performance on the core capabilities of the underlying self-evolving agents. Further analyses provide practical insights for future research, showing that execution-result-based supervision is particularly effective and that increasing supervision frequency yields diminishing returns. Together, these results support external LLM-based supervision as a practical approach to developing safer, more stable, and controllable self-evolving agent systems.

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