Your billing is pre-paid meaning that the date shown on www.spotify.com/account/overview is the day you will be billed again for the following month. To avoid this, all you need to do is cancel your subscription and revert to free before that day.
On a side note, $12 is the rate for iTunes subscriptions. You can sign up through Spotify directly to pay $9.99 a month and you may qualify for a special discount such as Spotify Student if you are enrolled at an eligiible institution of higher learning. Check your eligibility at www.spotify.com/student.