There is a chance the interface may vary for some reasons, but from what I can see on my screen, on My Music tab, there is a "Recently Added" section, followed by a section listing all your songs. For some people, the list is probably sorted by Artists - so tap on the section heading that says "Artists v" (with a downward arrow) to sort the list by artists, albums, songs, genres, or composers. You can also choose to show/hide iTunes purchases from here.
Sigh.. now launching this new Music app in iOS 8.4 seems to take forever, with it trying to get onto the internet and loading don't know what in the beginning before it decided to show all my offline, locally synced music. Listen to my own music also so gang koh..