On social media platforms, like Twitter, users are often interested in gaining more influence and popularity by growing their set of followers, aka their audience. Several studies have described the properties of users on Twitter based on static snapshots of their follower network. Other studies have analyzed the general process of link formation. Here, rather than investigating the dynamics of this process itself, we study how the characteristics of the audience and follower links change as the audience of a user grows in size on the road to user's popularity. To begin with, we find that the early followers tend to be more elite users than the late followers, i.e., they are more likely to have verified and expert accounts. Moreover, the early followers are significantly more similar to the person that they follow than the late followers. Namely, they are more likely to share time zone, language, and topics of interests with the followed user. To some extent, these phenomena are related with the growth of Twitter itself, wherein the early followers tend to be the early adopters of Twitter, while the late followers are late adopters. We isolate, however, the effect of the growth of audiences consisting of followers from the growth of Twitter's user base itself. Finally, we measure the engagement of such audiences with the content of the followed user, by measuring the probability that an early or late follower becomes a retweeter.