Yes, the filtered faceplate goes on the master socket. This is the ideal arrangement, but you do then need to do some extra wiring if your computers are elsewhere. If this isn't feasible then you really need to sort out your internal wiring I think. The big difference between using the test socket and using the normal socket suggests that your telephone wiring, or something connected to it, is the problem.
Just to be clear first, you haven't got any other telephone equipment such as a Sky box or a fax machine connected without a filter, have you. Sky boxes can be particularly troublesome, even behind a filter, and if you have one it would be worth disconnecting it to see if this helps.
If none of this applies then the wiring, or an internal source of interference, would seem to be the problem. One simple change which often helps is to disconnect the ring wire at the master socket faceplate. You can safely remove any wire(s) connected to terminal 3; just gently pull them out and bend them out of the way. It won't affect the ability of your phones to ring, because filters contain their own ring generating capacitors and electronic phones don't use the ring wire anyway.
Eric