Integrating a Magento theme into Joomla! is not as straight forward as it seems. Magento blocks are only shown on certain MageBridge pages, while Joomla! does not know how to handle empty bodies of Joomla! modules. Also, assigning a Joomla! module to certain MageBridge pages is impossible because the Joomla! Menu Assignment is just not flexible enough.
The best solution for all these problems is to add PHP-code to the template. But because Joomla! still does not know about the Magento theming logic, the MageBridge template helper-class MageBridgeTemplateHelper allows you to configure things while using fairly simple PHP-code.
Read more: MageBridge template helper