By default for membership and roles, the ASP.net infrastructure uses the default membership and role providers that stores that membership and roles data in different database. Run your application and if you register for a user from login page you can see the database at location "App_Data" folder created. The database is different hence the connection string is different. You are using entity framework so there are 2 ways to go from here.
1) Change the connection string and use the same default asp.net membership and role providers to store data in the database that your entity framework configuration is using. By this I mean the default membership and role providers use the database that you EF configuration points to.
2) Use EF to manage the membership and roles data. So the users and groups would be entities manages by the DBcontext as other entities.
I have recently implemented the second approach. The ASP.net membership provides hooks (extensibility) to implement your own providers and register them in the web.config file. Then create the User and Role entity and include them in DBContext. Of-course before registering the providers you need to implement them first by deriving from MembershipProvider and RoleProvider abstract classes. These classes are in `System.Web.Security' namespace.
You can follow this project for more details http://codefirstmembership.codeplex.com/
I believe the connections to separate database will not have any impact on the performance. As in the web model even if you use same database for incoming requests we have to make connections to database separately and the incoming requests can come concurrent. In fact keeping the database separate will take to database load to another server. But now you have 2 servers to back up and maintain. This will not be maintainable unless you want your membership data to be separate for some reasons like it is shared by other applications also.