So you solve the CF and then run the AddIn. Once you have the Edges table, it has the OID of the streets. You can join it to that streets feature class and copy over your TOID to the edges table. Then you can Join it to your external table based on this TOID.
Bring up the properties of the RoadLinks feature class. Then click on the Fields tab. It should show you all the fields that are present in your feature class. See if any of them are un-checked to hide them from view when you open the feature class. Most likely the ObjectID field has been turned off. if that is the case, check it on and now the values should be visible.