I wouldn't worry about a few unhappy leaves. I used to grow figs in containers further up north in a windy, exposed area. The leaves often got damaged in spring, but the trees bounced back.
Not sure about Stark Bros, but a lot of the nurseries around here get their fruit trees from commercial farms that are a few growing zones warmer. They truck them up all leafed out so they look attractive to consumers early in the season. Problem is, that means they're used to warmer weather. It can take them some time to harden off. That might explain the leaf damage?
Anyway, I'd say leave the little guy in part shade for two weeks, until it's putting out new growth. Then move it to full sun. Ultimately, your fig plants will want all the sun you can give them. And make sure it doesn't dry out. That's especially important for container plants - even more so for young ones.