Emergency response services are critical to public safety, with 9-1-1 call-takers playing a key role in ensuring timely and effective emergency operations. To ensure call-taking performance consistency, quality assurance is implemented to evaluate and refine call-takers' skillsets. However, traditional human-led evaluations struggle with high call volumes, leading to low coverage and delayed assessments. We introduce LogiDebrief, an AI-driven framework that automates traditional 9-1-1 call debriefing by integrating Signal-Temporal Logic (STL) with Large Language Models (LLMs) for fully-covered rigorous performance evaluation. LogiDebrief formalizes call-taking requirements as logical specifications, enabling systematic assessment of 9-1-1 calls against procedural guidelines. It employs a three-step verification process: (1) contextual understanding to identify responder types, incident classifications, and critical conditions; (2) STL-based runtime checking with LLM integration to ensure compliance; and (3) automated aggregation of results into quality assurance reports. Beyond its technical contributions, LogiDebrief has demonstrated real-world impact. Successfully deployed at Metro Nashville Department of Emergency Communications, it has assisted in debriefing 1,701 real-world calls, saving 311.85 hours of active engagement. Empirical evaluation with real-world data confirms its accuracy, while a case study and extensive user study highlight its effectiveness in enhancing call-taking performance.