Hello,
You need to use the importStyles method to import styles and use them. The method parseStyles is only to generate a DOCX with a preview of the existing styles and know which name and id they have and be able to use them.
Please run and check the included examples in the package to know how to use them, and also read the API methods (http://www.phpdocx.com/documentation/api-documentation) They explain how to use the methods and the available options.
Regards.