For older versions of
IntelliJ: Preferences > Inspections > JavaDoc issues > Declaration has JavaDoc problems
For newer versions of
IntelliJ: File > Settings… > Editor > Inspections > Java > JavaDoc issues > Declaration has JavaDoc problems
Make sure to move “scope” slider to desired level of visibility for packages, classes, methods, fields and inner classes, by default it is set to “none”. You can also set “severity” level.

In addition to continuous monitoring, you can also invoke inspections on demand with Cmd-Option-Shift-I, and enforce inspections prior to VCS commits(although it does not prevent you from committing your code with command line). You can also create specific inspection profiles, one for the university submissions, and another for your side projects, for example.
