Open profile settings by clicking Browser Settings button on the ribbon.

Select the profile you want to configure and proper command line parameter.

For Chrome specify
--incognito
For MS Edge
--inprivate
For Firefox
-private
For IE
-private
How it works. When Rapise launches a test, if required browser is not opened yet Rapise uses profile settings to launch a new process with specified command line parameters .
Also a test can explicitly open a browser with specified URL. If in this case browser is not running yet then profile settings are also used to start it.
Navigator.Open("http://libraryinformationsystem.org");
Video: Configuring Chrome Incognito Profile