I was concerned about this too, but after I finished connecting my personal page, there was a popup about which page to post to and I was able to select the business page. Haven't had a new campaign to test this out with yet.
Welcome back to the Community! Thank you for the great question! So when it comes to sharing an Email Campaign on a business Facebook, the business page must be connected to a personal page in order to post properly. This is to help guarantee that it is a real business page and not a scam or fan page. When you connect your Facebook to Constant Contact, it will show you the available profiles that you can post to.
Please let us know if you have any further questions.