The above responses by KMT are accurate. Custom Apps is part of the Apple Developer Program, and is simply a choice you make at time of publication under the Pricing & Availability section in App Store Connect. The review process is meant to be the same as the one you would go through for a public app. The reviewer will need to be able to fully use the app as intended, so please provide a demo mode or demo account for their use if they cannot create an account.
Your customer will need to install the app through ABM, and will need to have Custom Apps enabled there. Once you have entered their organization ID into App Store Connect when choosing private distribution, they should be able to see it in ABM for distribution to their users.
For more information, watch
Session 304 from WWDC19 and
Session 10667 available later this week