Member renewed without paying for another year term membership renewal

Hello,

I'm wondering if I messed up the configuration of our Membership options. A member recently emailed us saying his account was renewed automatically without him paying for another yearly membership. What we want to happen is that people's pro membership accounts expire at the expiration of their yearly term unless they renew by paying for another year term. Our settings for the subscription plan are this:

Serial
1 Year
PayPal Express - Single Payments Gateway

Should this be changed to Finite? Would they still be able to purchased a renewal if so? PLease advise.