Yup, that's right. If an effect applies to urban districts (or quarters), the tooltip makes it explicit - check Iguazu Falls, Pyramids or Muzibu Azaala Mpanga if you wanted to see what that looks like.
That said, there are definitely ways to make Uluru city work; you will rarely get more than 6-7 rural tiles in antiquity town, maybe up to 10 in exploration. If you can build up a city and still leave that many untouched, you have a good chance to claim them faster, so long as you can direct your buildings away from desert tiles (or if you have so many that it won't really matter).