Hello,
The parseStyles method supports paragraph, list and table styles, and the next version of phpdocx will include support for character styles. Sorry but we don't know what could be wrong with your DOCX and as the trial package is crypted it can't be debugged (payment licenses are open source (not free)). We recommend you to check the parseStyles sample included in all plackages, that include Word and custom styles.
Other solution would be using the DOCX that include the styles you want to use as base template with the CreateDocxFromTemplate class.
Regards.