Hello,
Unfortunately, if the emails were originally unsolicited SPAM and you clicked on the unsubscribe link in the email, you are simply confirming that your email address is valid, and they will share that with other spammers. It is never recommended to click unsubscribe in emails. The best way to unsubscribe, is to login to websites that you actually have an account on, and change you communication settings there. Those that you don't have an account on, or are randomly received SPAM messages, should simply be deleted.
For this particular sender, the best recourse is to setup a rule in your webmail interface or the Apple Mail application to quarantine or delete any emails from that sender. There are paid software applications and services out there that can help reduce the number of SPAM emails, like
SpamSieve (for the Mail application) and
Spamdrain.
Hope that helps.
C