To drill-down is a information technology term. It means to follow a hierarchy of records down from a general level to increasingly detailed level. It also applies to folder structures and hyperlinks. For example if you go to forum.wordreference.com (the top level of the forums) you could "drill down" through increasingly narrow choices until you reach a post on a very specific topic.
Wikipedia puts it quite well: "to drill down means to move from summary information to detailed data by focusing in on something".
What it means precisely in the topic text context, I'm not so sure. Perhaps it means he follows things through by narrowing down options in a logical way.