Registration with a choice of groups
Please navigate to Dashboard > Forums > Member Fields > User Fields Manager tab, edit the User Group field and make sure the custom usergroup you've created in checked in the Choose groups section.
First of all please navigate to Dashboard > Forums > Dashboard admin page. Click on [Synch User Profiles] and [Delete All Caches] buttons and check again.
Secondly, click on the "Synchronize" button on Dashboard > Forums > Usergroup admin page and check again.
Let us know the following information:
1. Navigate to Dashboard > Users > All Users admin page. Let us know how many authors you see.
2. Navigate to Dashboard > Forums > Members admin page. Filter users by role and let us know the number of the Authors here (on the screenshot I've select moderators as we don't have Author role):