Ticket-driven dialogues in cloud service systems, such as those in ByteDance’s Volcano Engine, are typically lengthy and fragmented. They are often interleaved across multiple evolving topics, which creates information overload, delays resolution, and risks obscuring critical details. While supervised or topic-aware summarization approaches can improve coherence, they require large annotated datasets and retraining, which are costly and poorly suited to dynamic environments. Zero-shot large language models (LLMs) alleviate these constraints, yet direct application to multi-party incident dialogues remains challenging due to overlapping voices, shifting focus, and substantial noise. To address this, we propose DIGEST, a topic-wise summarization framework that introduces hierarchical topic guidance into zero-shot LLM summarization. DIGEST first performs top-down segmentation to disentangle coarse threads and refine them into subtopics, then applies bottom-up aggregation to integrate local summaries into coherent narratives while preserving independence across issues. Experimental results demonstrate that it outperforms LLM-based summarization baselines.