There are two separate dedicated security roles for timelines: Timeline Managers and Timeline Contributors. If you wish to allow users to be able to contribute to timelines, you should ensure they are assigned the Timeline Contributor role for that area.
The social moderator security permission allows a user to moderate the timeline posts for all intranet areas. In the event a moderator doesn't have the permission to view the area in which a post has been reported, they will still be able to see the post in their notification.
Note: If Simplified Permissions are being used instead of Advanced, assigning a user group with the Viewer permission of an area will automatically provide them with the ability to post within timelines. If you wish to reduce timeline posts, you will be required to remove the user group and permissions from within the simplified permissions panel, and instead set the content viewer permissions within advanced permissions.