A wild guess ;-) Are the applications receiving an error message from the db at the point in time when you see more connection than no. of users??? The application may be coded to establish a connection for certian errors - 'unable to connect', 'time out' etc.
I would start with creating a Connection Event monitor to see when the connections are established, released etc and then compare the times with the application logs ...
"Most recent operation " in my opinion is not relevant to the problem you are facing ...