Why don't my work contacts appear in Contact Mover?

As of iOS 11.3, unmanaged apps can no longer access contacts from your managed corporate accounts unless your IT department allows it.  So if you have contacts in a corporate managed Exchange Server (Outlook) account, that account will not appear in Contact Mover unless you either:

a) Install Contact Mover as a managed app with the help of your IT department
b) Ask your IT department to "allow unmanaged apps to access managed contacts" as described here: https://support.apple.com/en-us/HT208749.  For those organizations using MobileIron, see this article: https://www.mobileiron.com/en/blog/Why-iOS-12-matters-to-your-organization