Private vialogues are searchable and users who come across them can request access, but you are the gatekeeper to your vialogue; you get final say over who can watch your video and participate in the discussion! You can grant or deny access in one of the two ways:
Go to your vialogue's settings page. You'll see the request(s) under the "Requests" tab.
Go to your notifications page. To get to this page, click on the activated Requests icon on your navigation bar and then click "More Requests".