Like I say, that's no how it works, they used to offer that service (iirc, as did Amazon), but discontinued it (presumably because they were hosting a lot of data, some of dubious provenance).
You have to sync your own music to whatever device (which is fine, I have everything I've previously bought on my iPhone, anything else I add to the library now magically appears and downloads for offline play). There should be an option when you first turn the library on to keep existing music on the phone. If you do, then anything you add outside of Apple Music behaves as music did before, hitting the sync button should send it over to the iPhone. You can combine your stuff with theirs in playlists. In practice, it's seamless.
When it works, of course. It lost all my playlists the other week. The solution was routine turn the library off and on. Fine, except all the Apple Music disappeared off my phone. It comes back but, ah, it's not downloaded. The only way to download everything, even if the auto-download option is enabled, is album-by-album. It's generally good, but there are petty annoyances like that (the main reason I plumped for Apple Musc is for it to play well with my current Apple stuff).