Sam,
With JLinked v1.1, the only time the profile can be imported is during the registration process. However, with the v1.2 release (coming out on Wednesday), we've added the ability to let the user choose to import their profile when linking their LinkedIn account with their existing Joomla account.
With the 1.2 release, the way this would work is that the user clicks the "Login with LinkedIn" button and are brought to the standard "Login or Register" page of JLinked. On the left-hand side of this page, they can choose to login with an existing Joomla user, and check the box allowing their profile to be imported. Once they do that, their initial profile will be imported and they'd be able to login to your site later on using either their Joomla (Active Directory) or LinkedIn credentials.
LinkedIn has the requirement that any profile information importing has to be explicitly granted by the user. Therefore, we don't do it on every login, yet. It's something we're working on, but to abide by LinkedIn's terms of service, there has to be some notice or way for the user to opt-in or out of their profile being imported.
Hope that all makes sense. If you have other questions though, just let us know!
Alex