OH Apple, this is so bad. Everything described here also happened at my side. Why are you not acting??? Here is my situation.
I waited for the Sonos integration and started Apple Music three days back with the family package. I have a carefully tagged library of 25k songs, 1430 albums that is. I read all the news about Apple screwing up tags in the icloud music library. I first made sure that there was no way Apple would affect anything in my Mac's library. Apple has an explicit statement that they would never change anything on your computer. Important for me since this is also the libary my Sonos system uses. Happy by this assurance, I turned on the iCloud music library. It matched around 17k songs which was done virtually immediately. There were around 8k songs that needed to be uploaded. I did not count the hours, but this probably took a day. Turned on Apple Music and iCloud music library on the iphone 6s and the iPad Air, both running IOS 9.2.1. It all looked great. iCloud music library indeed screwed up tagging wise, but that was expected and somehow also understandable given the matching principle Apple uses. Sonos integration is perfect so one happy camper.
Then this morning I was warned with no memory on the iPad and a full iCloud backup which is impossible since I always keep enough buffer space. It appeared that the iPad started to download thousands of songs from my library. Stopping did not help. If I turn off using the iCloud music library it is automatically turned on again when opening Music. End result, iPad complete full. I started to delete music from the Settings menu. Every time Music keeps coming up with the downloads. To me it seems that Music tries to download all the songs that were unique to me, so the 8k that were uploaded from my Mac to the iCloud music library. No 100% proof yet, but virtually sure. I tried everything, restarting, killing Music, turning of Apple music and iCloud music library, cancelling the downloads, etc. They keep coming back! I now decided to just download 8k of songs and every 10GB just delete the music. Let's what uses after that. To me it seems that within the copy of the library on the iPad locally, some settings are going wrong. Something here furthermore screwed up the iPad badly. It cannot even check for a software update anymore. My next attempt would be to clean up the whole iPad and restore a backup. If anybody has any suggestions, please!
Then the iPhone. The downloading also started there when I opened music. I cancelled the download. After that nothing happened anymore. For a number of hours it is now quiet there, so all OK. Strange given the above.
TO APPLE: to me it seems that the issue here is twofold. First local music libraries somehow getting corrupted, and second all of this seems to be caused by music that is not matched and was uploaded to the iCloud music library. With a 100k songs per person guaranteed capacity this must be a HUGE issue to Apple and I hope it is treated as such.