CANCEL YOUR CARD! Call your bank/credit card service and explain it to them! Put a hold/block on your card and receive your new one. Trust me, pretty soon the magazine company will be trying to get ahold of you...then you can cancel. Whatever money you still owe, only pay in check or cash. Do not give them your card number!
I think I made a similar mistake with the same people. I on the other hand was duped on my own stupidity. I didn't have any magazine subscriptions and I didn't want any! But...the salesman was so sweet and we talked a lot about school and his family and crap like that (he was an elderly man, so it wasn't creepy flirting). But we held the same spiritual beliefs, he was an old vetran, etc. He was a sweet guy and I felt really bad denying him after he spent so much time talking to me. I shouldn't have talked to him! He was a nice guy, but I wouldn't have known that if I would just have said, "Sorry, not interested." and hung up. Problem solved. But, I didn't. I made an order. Then using the number he gave me (I have since lost said number), I called back 20 minutes later and canceled. The person on the phone said the cancellation had been made, but I have already paid for the first magazines. I should have argued with her...but I am young and stupid.
The next month I received some magazines. Okay, awesome. Then I got some more. And the next month I got even more! I freaked out! I am a college student, living paycheck to paycheck!! But...stupid me decided I enjoyed the magazines...so I just kept receiving and reading. Money was getting even tighter, and then I got a phone call from the company saying that I could pay the total due upfront and save a lot of money: $400-500 (somewhere in there). Well, I didn't even have that much in my account at the time, so I immediately broke in to tears telling him I couldn't do it! I demanded they cancel it like they were supposed to and I was so angry! He then asked if I wanted to switch magazines. I stopped crying and got angry. He explained to me I didn't owe $400 but I would end up paying that much by the end of my subscription. I canceled completely. He explained I would get the last magazines that I paid for. Okay.
I continued to get several magazines. I think they say things like, "You'll receive the ones you've already paid for" so that when they come in the mail, it takes us awhile to realize they're still charging! So sneaky! So I called and canceled my card. They can call me back at their own risk because I will chew them out.