With multiple mailboxes the Base Mailbox Introductory Greeting is only active if you are not using the Distinctive Ring service or if you turn off the Distinctive Ring feature. In that case, the Base Mailbox Introductory Greeting will be played when the phone is unanswered so callers can select a mailbox for their message. If you do not wish to record a personalized Introductory Greeting for your Base Mailbox, you can use the message that comes prerecorded with your Multiple Voice Mailboxes. If callers hear your base mailbox greeting and do not press an option to be connected with a personal mailbox, they may leave a message in your base mailbox.
Why do I have to have a different password for each mailbox?
How does Enhanced Voicemail with Distinctive Ring work?