Same issue here. This download-until-the-phone-fills up has happened to me 3 times now. Once after an iOS update, once after I rebuilt my itunes library on the master machine, and now after the iOS 9.3 update. It is insanely frustrating -- the phone is rendered useless for hours until it fills up and errors out, as everything becomes so unstable and slow. It turns into a toaster from all the processing. If you happen to be on metered-internet or cellular get ready for 10s of gigabytes of data usage. This is potentially a very expensive bug for some. The remedies all involve destroying and effectively rebuilding your phone's music library and potentially all iCloud data. This all typically occupies hours of my time to return to a usable phone.
In addition to the "total" scenario, all music in my library is constantly "double" downloading. No fix I've found for this other than just not storing anything on the phone itself, which really limits the usefulness of this.
This is one of the worst bugs I've ever encountered in consumer software. Unbelievable.