How do I separate Various Artists

[Boom-bap]

Here's an example:

I downloaded Monstercat compilations, and when I check out the songs (all songs and/albums) their respective artists are labeled under, but when I go to Music Library -> Artists, those artists are not there, only Monstercat.

ADDITIONAL DETAILS:
Tapping "Go to artist" on a song works.

Downloading an extra song from a different place/source makes that one artist appear. But I don't want to have to do that for about 20 different artists. How do I put them under the artist label?

 

[B. Diddy]

Welcome to Android Central! Which music app are you using, Google Play Music or something else? Are these compilations from Google Play, or are you downloading them from somewhere else?