If you unsubscribed from their E-Mails and they kept sending you those unwanted E-Mails AND they even admitted their mistake then you have a case in court because they may have broken anti-spam laws as well as tormenting you. I would think. I would seek advise from a lawyer to confirm that suspicion, though. I would definitely be angry if that happened to me. They don't really seem to care about taking responsibility for their mistakes...
It's automated once you unsubscribe to their newsletter and the database is updated they cannot send you any more emails, they have a broken system if the emails keep coming in even though you already unsubscribe, they are violating the anti-spam law if you do not subscribe but receive a lot of fo emails.
I figure that the promotional emails are ready to sent on a given date and it was too late to replace the date, sometimes it happens to me after I unsubscribe I still receive one or two emails because it was already set to be sent.