Apple Music

I am having a problem with overlaying my videos on my iphone with my own music. I recently obtained a new iphone after I destroyed mine and logged into the icloud to download all of my apps, music, pictures, etc. I like to overlay videos with my music but, everytime I attempt to use a song, my phone states that the song is stored in the cloud and i must download it. So, I go to my music, click on the download icon and then the song appears with a a check mark inside of a phone next to it. Then I attempt to use the song again, and I get the same message. What can I do here? I am so lost haha