Ashley,
You don't state exactly what kind of tape drive you are using. The autoloader offerings from Dell often won't automatically eject the tape, you have do unlock the tape drive in BE, then use the tape loader menu to export the tape, import the replacement tape, then go back into BE and lock the tape drive to control it with BE, at least that is how it works with the PV-122T unit. If it is a single tape drive then you might be able to use the BEMCMD process to eject the tape.
Dell can right the utility to directly access the tape unit, BE doesn't always offer that kind of control due to the drivers used.