When a user accepts an invite, by default they will receive a welcome notification when they first login to the site. The type of notification they receive is set by the discourse narrative bot welcome post type site setting. This setting defaults to “Start the new user tutorial for all users”, but it can be set to “Send all new users a welcome message with a quick start guide.” This welcome message will usually not be emailed to users, they will see the notification for it when they first login to the site:
There are a couple of site settings that could be affecting this on your site. The disable discourse narrative bot welcome post site setting completely disables the welcome message. The discourse narrative bot welcome post delay site setting delays the welcome message so that it is not immediately sent. This setting defaults to 0 seconds (no delay.)