While browsing the source code, SonarQube in IntelliJ highlights issues. But its added value is to be able highlight the new issues that you have introduced while adding/modifying the source code. You can thus check your code prior to pushing it to the SCM to make sure that you haven't introduced any new issues.
Running an Analysis
To run a new analysis, right click on your project, go to Analyze > Run Inspection by Name..., search for SonarQube Issues and run the analysis on the whole project.
The analysis mode is incremental. Because only new/modified files are checked, you get feedback and the list of new issues very quickly.
Browsing the Issues
The list of issues can be browsed in the Inspection Results for Inspection Profile 'SonarQube Issues' panel (View > Tool Windows > Inspection). Issues are flagged in the source code viewer.