The eject function is usually used with stand alone tape drive and not libraries and does prompt for action (by design) as with a stand alone drive, the tape is lifted slightly out of the drive and then needs human interaction to remove it and insert a new tape for the next job.
Libraries do not keep tapes in the drives as they move then back to storage slots. To get tapes out of a library you use the an Export job/function as long as a Mailslot or Import/Export slot is available and configured correctly) What the Export does is move a tape from a storage slot into the Import/Export slot so that it can be removed. I am not sure if this generates an alert to acknowledge as jobs can still use further tapes from the storage slots so any alert is less important. An Import just moves the tape from the Import/Export slot back to a storage slot.
One final point if you always store the tapes that are removed from the library in the same place then you don't really need custom Media Vauts as BE will mark the media as Offline when it is not in the library. Media Vaults are useful so that you can easily see which tapes are (for instance) on a shelf in your server room vs in some form of offsite storage as you can use them to remind you where specific tapes are located when they are not in the library.