The issue has to do with where you are merging the styles for the SSN control and parts (i.e. the ThemeResources.xaml) file. Our Sample Browser loads the files up as part of the WPF theming system. This means that the Styles can be applied as "default" styles. The way you are merging in the ThemeResources.xaml file, the styles can only be applied as "implicit" styles.
Basically, you would need to create a folder called "Themes" in the root of your application's project. Then create a Generic.xaml file in that folder, with the following contents:
This will allow WPF to load up the ThemeResources.xaml properly. You can refer to our SampleBrowser to see how we did it there.