Apparently, when the template is put on the page, [[X
does not exist, but [[X]] does exist. Later [[X]] is changed into a
disambiguation page and [[X (district)]] is created. However, the
links table is not updated in this case. Is there a way to force an
update of the links of a set of pages to be forced (or at least put in
the job queue)? In the past this could be done with a touch
(zero-edit) on the page, but that doesn't seem to work any more.
Looks like it's working fine to me... in the example you gave, the
(district) page exists, and is linked to... Can you give an example of
a page that isn't working?