On the surface of it it looks like something is causing the system to run a full  map reset.  As I don't have a network set up it is difficult for me to run tests on this.

The first time you use the maps on the second and subsequent workstations I would expect that you would need to  go into map options. There you should  see the base map selected for the first workstation. Make sure that you select this (don't create a new one).  Then choose 'reset', but at the next screen (Confirm) you must select 'Yes' and not 'All'. This should copy the required files into the appropriate place on the workstation and add the required entry to the Computer_Map table, but it shouldn't overwrite any polygons or polygon layers already created on the first workstation.

If you are not seeing the screens as descibed above, or if you are following  the above procedure and not getting the expected results let us know. 

Any polygon layers or polygons you create should  be shared between all users, however, background layers (eg map tiles)  will not be shared and will need to be set up on each machine.  If all workstation  can't see the polygons or polygon layers, then  I think two things are worth investigating. Firstly, are they all  using the same base map, and secondly   is the Object sheet folder on the server and do all the workstations/users have read and write permsions on the folder.  It would also be worth checking that the registry value for the Object Sheet file Path is set to point to the same place on all work stations (HKEY_CURRENT_USER\Software\Dorset Software\Recorder 6\Settings\Object Sheet File Path)

The polgon boundaries are not stored in the database tables, but in the various files in Object Sheet folder. Adding a new polygon to an existing polygon layer will affect the file for the polygon layer, but will not add change the tables.

After you have added the second work station and chosen a base map you should  end up with a new entry in the Computer Map table, identified by the computer name of the workstation. This should have the same base map key as the entry for  original works station. The Base Map and Map Sheet tables should not change.

If you add an additional polygon layer to the base map then you will get an additional entry in the Map Sheet table for the polygon layer.