OK, I see where the terminology problem is happening. Let me try a breakdown like this, just to make sure we're all on the same page:
Central Servers: A plural term that identifies the 3 servers the Corp begins the game with - R&D (Draw Pile), HQ (ID & Hand), and Archives (Discard Pile)
Remote Servers: A catchall term for any and all Servers that are built after initial setup. These are defined as the placement of a facedown card (That may be either an Agenda or an Asset) and/or the establishment of an ICE defensive line. Remote Servers exist as long as one of these two elements is present.
Server: A term given to represent any and all "locations" in the Corp Player's play area that may have a Run activated on. All Servers are either Remote Servers or Central Servers, based on how they are established during game play. Any card that targets a "Server" is valid against either of these game elements.
Therefore, you are not establishing "Sub-servers" in a singular Remote Server. Rather, you are building multiple Remote Servers, with each one holding/maintaining an Asset or an Agenda.