maybe you have 'sync over cellular' accidently enabled in spotify settings when downloading data for offline use..? with offline mode enabled most of the time I've never reached even 100mb mobile data usage by spotify during a month.
btw - if your memory is full it can make any app or whole system to act weird or not working properly.. so my advise would be to wipe spotify data (in spotify settings), create new 'backup' playlist with size that will fit your backup phone, download over wi-fi and enable offline mode.
Maybe the phone just downloaded music for your playlists and it will take up bandwidth. After the songs have already been download, it will no longer use data that is as big as that. If you set it to high quality, downloading 200 songs will likely use 2gb of bandwidth to download. Before Offline mode will work, Spotify will need to download data. After that, the data can already be used offline. Just remember to always turn off mobile data to save battery and not use the limited given by your carrier.