Yes it is the router is reading / writing NTFS, not the computers.
If the router is sharing the drive using SMB (sometimes called Windows file sharing even though it not specific) the following applies:-
On your Mac, the router will show up as a networked computer / server icon (often a Windows bluescreen style icon).
The share will appear as a folder inside that. Depending on how the router handles it it will present either the whole drive or a folder (and everything under it).
Same with Windows and Linux
You can help things by making sure the router, Mac and Windows all have the same WorkGroup setting (Window 8 confuses things by instead pushing the HomeGroup concept to the fore and hiding some of the (Home/Private or Public) what-kind-of-network choices).
On Mac and Linux the "filesystem" of the shared drive will show as SMBFS or equivalent regardless of how the drive is formatted.
If the underlying service on the router is Samba, it would allow you to setup multiple shared folders with different group/user permissions but the router's WebUI might only offer simplified options.
Personally the way I might use a router with USB drive sharing would be to plug in a USB stick (16/32GB or so) and use it for secure remote access storage (if the router can also run a VPN service).
I think 12MB/s will be too frustrating for a 2TB drive (2 days continuous to fill it so once you have tested it works you should probably pre-populate it while attached to a computer!)
prompt $P - Invalid drive specification - Abort, Retry, Fail? $G
prlzx on iDNET: ADSL2+ / 21CN at ~4Mbps / 700kbps with IP4/6
Edited by prlzx (Sat 09-Feb-13 15:31:01)