HI there!
We have different problems as I didn't sign up for Apple Music and didn't encounter the iTunes Match prompt that you have.
As for Apple Music and offline files, i understand that Apple Music subscribers can choose only songs they want on each device to be downloaded onto it. So it won't try to download your entire collection onto your device(s).
With regard to the problem I have to manually copy music onto my iPhone 6, unfortunately the problem remains after restoring the phone and all the other suggestions kindly offered by Jamvan. BUT, I stumbled across a workaround.
1. With iPhone plugged in to the Mac and iTunes running, select a bunch of albums you'd like to copy onto the device. Looking at the music on device in iTunes, all these songs will be grey with a circle on the leftmost column (meaning yet to be copied I assume). Though the top status bar says preparing to update, it never proceeds to copy.
2. Next I eject the phone, unplug it from the Mac and quit iTunes.
3. Launch iTunes and plug in phone.
4. Go to music on device and you should still see the new songs to be copied are greyed out. Delete one of them greyed ones and it should trigger an update. The rest of the songs you dragged to the phone earlier will start copying (finally!).
5. however if you have more to copy that what albums you have selected in step 1, be sure to drag and drop them to the device while step 4 is still in the midst of copying! That way you don't have to start from step 1.
Hope that helps someone. 🙂