I've created www as a cname pointing to example.com, but it seems to use the default theme instead of the theme I've configured for the example.com domain.

My advice has nothing to do with the Plugin itself: I'd set up the web server (Nginx or Apache ?) so that either www.example.com REDIRECTS to example.com or vice versa. This is also helpful in other aspects, f.e. SEO.

Thanks, that is what I've ended up doing in Nginx.

My advise is to redirect example.com to www.example.com ... There are a lot of reasons to use www. in front of your domain. I did web dev for years before I realized any of them... but do it. (google it if you want more info)