The workflow for activating the level symbology overrides correctly for the Drawing Views and Sheet Views is as follows:
1. Go to the Drawing View
2. Go to Home > Primary > References
3. Double-click on the Reference's Presentation type and it should open the Reference Presentation dialog box.
4. Then turn on the Level Overrides, and click Ok.
5. This should activate the Level Overrides for the Drawing View and the corresponding Sheet View as well.
This workflow only turns on/off the level symbology for Drawing View selected and not all Drawing Views.