Confused by clouds only on iPhone

I have all my music that I downloaded or put on myself in my iTunes Library, on both my iMac and iPod. I recently got my first smartphone and immediately much of my music showed up on the phone. But all songs have a red cloud say I can stream these. I don't want to use iCloud. I don't have to stream nor do I want to do that. I bought these songs and they are in my library on my Mac and iPod as well as backed up on external drives. What must I do to just simply get them to my Pro Max iPhone...just synch? I'm concerned I might do something wrong.