Understanding an unfamiliar codebase is an essential task for developers in various scenarios, such as during the onboarding process. Especially when the codebase is large and time is limited, achieving a decent level of comprehension remains challenging for both experienced and novice developers, even with the assistance of LLMs. Existing studies have shown that LLMs often fail to support users in understanding code structures or to provide user-centered, adaptive, and dynamic assistance in real-world settings. To address this, we propose learning from the perspective of a unique role, code auditors, whose work often requires them to quickly familiarize themselves with new code projects on a weekly or even daily basis. To achieve this, we recruited and interviewed 8 code auditing practitioners to understand how they master codebase understanding. We identified four design opportunities for an LLM-based codebase understanding system: supporting cognitive alignment through automated codebase information extraction, decomposition, and representation, as well as reducing manual effort and conversational distraction through interaction design. To validate these four design opportunities, we designed a system prototype, CodeMap, that provides dynamic information extraction and representation aligned with the human cognitive flow and enables interactive switching among hierarchical codebase visualizations. We then conducted a user study with nine experienced developers and six novice developers. Our results demonstrate that CodeMap significantly improved users' perceived intuitiveness, ease of use, and usefulness in supporting code comprehension, while reducing their reliance on reading and interpreting LLM responses by 79% and increasing map usage time by 90% compared to the static visualization analysis tool.