Your post is unclear. To listen to music from your CDs on your iPhone, you must sync the music in some way.
If you have an Apple Music subscription, and are also using "Sync Library", then I believe that your iPhone and Mac will sync their Music libraries through "iCloud Music Library". However, if you stop subscribing, any synced copies will go away or stop working.
If you have an iTunes Match subscription, I believe things work in a similar (though perhaps not identical) fashion.
An alternative is to manually sync your iPhone to your Mac. First you would import music from your CDs into your Mac's Music library. Then you would connect your iPhone to your Mac with a USB cable, select your iPhone from the sidebar in one of your Finder windows, select music to load onto the iPhone, and do a synchronization. (That option is available even with an Apple Music subscription as long as you keep "Sync Library" turned OFF on both the iPhone and the Mac.)
With manual synchronization, music from your own CDs, that you are listening to on your iPhone, is stored locally, on your iPhone. However, you need to go through your Mac (or Windows PC) to put it onto the iPhone in the first place – and you should keep the copies on your computer, so that if you want to update the iPhone again, with a slightly different selection, you can do so.