It sounds like the receptionist answers a call, places it on hold, then uses overhead paging to alert an employee that he has a call.
Problem is, the only phone he can get to is programmed to hotline dial the operator.
So the employee can't pick up the handset and dial a pickup code, the hotline function takes priority.
So the hotline phone phone tells the operator which extension he has picked up, so now the operator can pick up the call and transfer it to the extension. When a hotline extension rings, the incoming call takes priority over the hotline function.
I can't really think of a solution, except to disable the hotline functionality, and use a hardware solution. Zoom used to make a "hotshot" dialer which would dial a preprogrammed number upon lifting the handset, but it could be set to wait a few seconds after dial tone to allow the user to overide and dial their own number. Maybe Viking Electronics makes something that can do this?
I guess maybe we should ask why the hotline? To keep the users from dialing other extension numbers or outside numbers?