Changes made to the templates apart of your campaign will ONLY show up if the email has not been created/scheduled yet. Check out the diagram below to see what happens on day one of a three-step campaign.
As you can see, once 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.