Short answer, no. It’s by design.
The longer answer though, is this.
The application performs real-time tracking of activity in your ‘Mentions’ and ‘Messages’ columns. It uses identifiers embedded in the content in these columns to determine what is new, and what is not whilst performing this tracking and stores the last identifier for each column in a configuration file.
The first time you run the application, the configuration file does not contain these identifier and so the application deliberately doesn’t notify you of new content because it’s not able to determine what’s new. Once the application is run for the first time though, these identifiers are stored, and tracking begins!