Please provide us more information. A class library isn't an executable and therefore should never run in VS directly. To run a class library you need a host project such as a console or winforms app.
What it sounds like to me is that you have a web app (that happens to produce a DLL but isn't a class library). The web app, when run in the debugger, is run depending upon your launch.settings file. By default it'll auto-start IIS Express and then open the browser, also configured in VS, and connect to the site. The version of the browser used by VS is generally an isolated instance that is independent of your actual browser (eg. Chrome).
Please provide more information such as the exact project type you're trying to run, what behavior you're seeing, any errors or output from the output window and ideally some screenshots or something to help us understand your issue.