Every client has unique HW ID. Client count is based on this HW ID. HW ID is transfered in IEngine_Connect() (InitClient()) to AFIS. So "client count"  on ExpressID AFIS is amount of connected machines/servers. When you use multiple IDKit connections/instances from one machine/server it increments the "client count" on ExpressID AFIS only by one.
When you disconnect from client, you cannot see it immediately in AFIS log (Client count), because it's cached for one more hour.