Those 8 streamed songs shouldn't be stored on your phone just because you streamed them.
Once Match is active and everything is in iCloud (unless you manually download songs) streaming them will not put them on your device.
Check again in Storage and if you spot Music go to it and delete everything.
Check again in iTunes in the iPhone page On My Device section if there's anything in Music repeat the above.
I think it was temporary, the About isn't very reliable in my experience, what's reliable is Storage and iTunes. If there's nothing there then there's nothing.
Or they're ringtones, ringtones are stored locally on your device, always no matter what.
Check Tones just below Music in iTunes, if those 10 songs are ringtones...
Side note: ongs purchased from iTunes Store and matched in iCloud also stay on your device, because you purchased hence downloaded them on your device, unless you remember to go to Storage and delete Music.
And yes you can download songs from iCloud on iPhone, whichever song you're "on" in a list, there's 3 dots --- on the right, tap and choose Make Available Offline. That will download the song locally so that you don't stream it but store it.