Android's Earthquake Alert (AEA) system provided timely early warnings to millions during the Mw 6.2 Marmara Ereglisi, Türkiye earthquake on April 23, 2025. This event, the largest in the region in 25 years, served as a critical real-world test for smartphone-based Earthquake Early Warning (EEW) systems. The AEA system successfully delivered alerts to users with high precision, offering over a minute of warning before the strongest shaking reached urban areas. This study leveraged Large Language Models (LLMs) to analyze more than 500 public social media posts from the X platform, extracting 42 distinct attributes related to user experience and behavior. Statistical analyses revealed significant relationships, notably a strong correlation between user trust and alert timeliness. Our results indicate a distinction between engineering and the user-centric definition of system accuracy. We found that timeliness is accuracy in the user's mind. Overall, this study provides actionable insights for optimizing alert design, public education campaigns, and future behavioral research to improve the effectiveness of such systems in seismically active regions.