Pay for sins versus take our place?

This morning while visiting a church, I heard something interesting in a Sunday School class that bears on struggles I am currently having over the concept of the atonement. The teacher said that he believed that Christ paid for the sin of everyone, but only took the place of those who believe on him. When I questioned him on what he meant, he said that he meant that the atonement is effecatious only for those who believe. I do not think that he really understood what he had said, or at least how it had come across to me.

If I take what he said literally, there is a difference between Christ paying for sins and Christ taking one's place. That could speak to the nature of the atonement: Christus Victor or penal substitution.