In Adobe Story, notifications are messages used to provide information on shared documents/projects, and the comments and edits posted on them. While comments and edits are displayed to other users almost instantly, a notification on comments is sent only after a user closes the document.
Notifications for offline documents are sent when you switch Adobe Story to the online mode. If you switch to the online mode just after signing in to the offline mode, offline notifications are sent when you open any document.
If any shared document is open when you switch to online mode, notifications are sent when you close the document.