Changes made to the templates that are part of your campaign will only show up if the email has not been created/scheduled yet.
The diagram outlines what happens on day one of a three-step campaign.
After the first email is sent out, the following email will be immediately created and scheduled to go out. Any changes made to Email B at this point will not be reflected when it is time to send. You will need to cancel the campaign and rebuild it starting from the updated version of Email B.