If you have a component written by a third party developer then by default this migrator will not transfer their data. However the developer of your component may have created some migration plugins that you can install that will include the component in the migration system. There is a section of the Joomla! Extension Directory specifically for third party extension, transformation and load plugins.
JED Migrator ETL Plugins (new window) >>
You can install extra plugins by doing the following:
At this point when you run the migration script the third party component's data should also be exported.