I'm having the same issue. Just got an alert that I used 7GB of data (95% of it was Spotify) in 10 days. All the music I listen to is offline. I reset all stats, listened to offline-only music for 25minutes and ended up with 42MB of Spotify data usage.
My issue earlier this year (insanely high data usage, even when listening to already saved music) was fixed by a Spotify update. The issue was although the music is saved to your device, the album artwork isn't, and it got stuck in a loop of trying to download the artwork but failing. It would happen continuously, so I was essentially sucking data from the ether as fast as my provider would allow. Would rack up over half a gigabyte in less time than it takes to walk to the shops.
My advice is to notify support/accounts, turn off mobile data for Spotify and hopefully they have a solution soon. Keep a record of your data usage (iPhone will track how much data each app is using, but you need to clear it manually, so maybe try taking screenshots of the data use every few minutes if you need to demonstrate what's happening). I also gave them copies of my phone bill which itemizes data use in blocks, and there were periods of about fifteen minutes where every minute would use EXACTLY the same amount of data (around 52MB), and would only happen when I was out of the house... listening to Spotify.
I found that the customer service was reluctant to provide any sort of compensation for the insane data usage, they eventually offered me a free month, but seeing as I had racked up over three gigabytes of data use over my plan, I didn't budge and they finally offered me three which I took. So my advice:
1. Turn off mobile data
2. If neccessary, track your data use and be thorough with it
3. Don't take measly offers if their bug is costing you considerable money
Yeah, seems like the exactly same problem as on my phone, since artworks are always disappering when opening the app after few minutes. It probably just downloads all songs from the internet, even though all of them are saved in my device in the highest quality...
Cleared roaming data and streamed one song with data usage reaching 120 MB. As mentioned earlier, the data usage is extreme. For this became an issue when upgrading to the new iPhone 7. Haven't changed any of the settings.