I'm in the UK. [...] The extension plug is an RJ14, but the
> splitter's socket is an RJ11 (2 pins instead of 4). [...] But
> here's the weird thing -- the ADSL connection works fine when the
> modem's plugged into the upstairs socket.
Are you sure that's actually a splitter, not a microfilter? It sounds from your description like the upstairs socket was installed for ADSL use with a microfilter on the master socket -- an arrangement that was pretty common in the early days of BT ADSL. Some models of microfilter do look very similar to regular splitters, except that they have an RJ11 for the ADSL modem rather than a normal BS6312 phone socket.
Adam Sampson