The Active Directory Computer information (For the computer object) updates at the interval set by that client setting you mentioned.
The Active Directory User information (For the logged on user) updates when the user logs in.
It looks like this in the client log:
At 15:10:28 -0500 -
User interface process started for user ‘strawgate’
At 15:10:39 -0500 -
ActiveDirectory: User logged in - Domain: AD User: strawgate
ActiveDirectory: Refreshed User Information - Domain: AD User: strawgate