It appears that objects like Announcements scheduled for future display, or deleted Announcments, are still in the database and so the search engine is seeing them and displaying them in the feed. The Search engine is probably not programmed to know the logic of each module, like the Announcement module, and the field to "display at a future date/time".
Seems there needs to be a way to MARK an item, record or object in the database as Do Not Index. In this case, for example, an Announcement scheduled to be displayed at some future date/time would be flagged for the Search engine to ignore/do not index, until such time as the flag is removed, then Index this item and show it in the feed, too.
I am not sure exactly how things work under the DNN hood, but this could explain the slow/no feed update issue.