When constructing a resource extractor, like a mine or a farm you have 2 options:

1 Build it through the city build interface

2 Build it by clicking on the resource tile and clicking the build button

Now the bug/exploit seems to be that an extractor built as part of the city actually uses some of the improvement tiles of that city; while an extractor built using the second method does not claim any tiles from the city, thus allowing you to construct something else in its place.

There is a minor difference in that city built tiles get a city wall, while the stand-alone constructions do not normally get a wall. However, you can grow a city around a stand-alone extractor to get it into the city walls as well (at least graphically).