Adding tracks on iMac is also downloading them.

Hi there, Forcefour.

It appears that, iTunes on your iMac, isn't working as expected. When you add a song from Apple Music, it automatically downloads it. Good job in figuring out how to remove it, and I'm happy to help.

Please check to see if you have automatic downloads turned on.
Turn on Automatic Downloads for iTunes Store, App Store, and iBooks Store purchases

iTunes

1. Open iTunes. If you haven't authorized your computer, choose Store > Authorize This Computer from the menu bar at the top of your computer screen.
2. Mac: From the menu bar at the top of your computer screen, choose iTunes > Preferences.
Windows: From the menu bar at the top of the iTunes window, choose Edit > Preferences.
3. Click the Downloads tab, then select the content that you want to automatically download.

4. Click OK.

If Music is checked, uncheck it, click OK and then try to add another song to your library.

Let me know how that goes.

Take care!