Why WAIT_TIME_MICRO is greater than IDLE_TIME?

My DB version is 11.2.0.2. The IDLE_TIME in the default profile is set to 30. A user/schema has the default profile. The user has a Windows service connecting to the DB. I often see many VERY old sessions from the service accumulating until the DB issues ORA-00020 (max # processes exceeded, all process state objects are in use). I guess the service is not using connection pooling, but my question is why the DB does not kill the old sessions when they have waited more than the IDLE_TIME. These sessions have the following measure:

WAIT_CLASS = Idle

STATE = WAITING