Looks like the css/skin is not getting included in the corr for the included section.
You can do the following. Go to the skin and under other actions > click preview. Copy the code and enter the same in a non auto generated section within the <style> tags and include this section in the section you are using in the corr rule.
This should enable the css for the section.
You can verify the same by opening the corr after it is sent.
I am not sure if it would still display correctly in Outlook since Outlook on Windows is not able to handle the complex CSS auto generated by the skin rule form - this has been an issue for all the Outlook version - developers are dealing with this issue by using some custom CSS for outlook > http://templates.mailchimp.com/development/css/outlook-conditional-css/ - Issues related to CSS support with Outlook should be directed to Microsoft.