When the text in a names field for the polygons is changed/updated in the default copy on the network server and versions are reconciled and synchronization is run, those changes “flow” to the polygons on the local (child) GDB but not to the feature-linked annotations based on those same polygons in the child. The work around we were given was to do a join to the feature-linked annos and calculate column to update them. It is very time-consuming having to run this procedure individually to update annos on each of our 220 maps in a series. The replication system should be able to update these annos automatically, because of the relationship class/link. If users have similar need/experience, please share a comment below.