The problem with atonement - universal or limted?

From an online reviewer -

"To develop my one criticism a bit further, I found in Derek's book what I have found in other books on the cross, that is a clear inconsistency between their view of the nature of Christ's death and how it relates to salvation by faith. In brief, it's simply inconsistent to believe that Christ died in the place of people as a payment and to say that those people have to believe in order to be saved, that is, freed from the payment. Why? Because if Christ's death is by nature a matter of payment wherein he is in effect paying off the "fine" due to your sins, upon paying off that "fine" you hardly have to believe in order to freed from the fine (i.e., saved). Freedom from punishment would be an automatic effect of Christ's death if Christ was paying off your fine on the cross. It's no different than if I pay off any of your debts (credit, legal, personal, etc.), my payment automatically frees you from the obligation to pay regardless of your trust or non-trust in me. Thus, there is no need for faith to be saved since one was saved automatically. This unfortunately is the problem that Derek runs into in his book. I was hoping that he had recognized the problem with the traditional explanation of a vicarious death and given a solution to the problem, though he does not..., but again, unfortunately Derek didn't really recognize this problem. Aside from that, the book has a lot of great information both theological and practical."