Sold an iPhone and I keep getting their messages?

Hi, I sold a sprint iPhone 4 and I think the guy activated it. I'm not sure. I did not restore it I simply deleted everything and signed out of everything. Couple weeks later I get a pop up badge that says number *** is associated with my iPhone, the one i sold, and did I want to connect it with this apple device. I said yes not knowing what it would do an shortly after I started receiving messages from numbers, numbers not saved in my phone. And it said I sent them. But I didn't. I looked at the sending and receiving addresses and the number of the guy I sold it too was listed under both to send and receive, so I just put I to receive and not send so I can still use my number and text my friends. How did this happen?

Easy, you were stupid enough to not do a factory reset on the phone.