Display Custom Fields in Activities in Views
Nope.  That is not expected behavior.

If you have two separate databases, one for Drupal and one for Civi, then you'll need to add the tables to the settings.php file.  Until you add them, Views will show the fields as available but will display an error that the table could not be found.

Every time you add a new custom set of fields, you'll need to go to Admnister/System Settings/CMS Database Integration, copy the code there and paste it into your settings.php file.