If your Kiln has 2 adjacencies then a specialist there gets 2 science and 2+1=3 cultureYes but the bonuses do not change dramatically tile from tile. What I am suggesting would be to place an “artist” on the kiln for +5 culture. Instead you get 2 science, 2 culture, 2 gold, etc. That is what seems general to me. Basically you just choose the best overall yield. It would be more interesting to say: I really want this city to focus on culture, so I will place artists here.
If your Library has 2 adjacencies then a specialist placed there gets 2+1=3 science and 2 culture (if you also have an academy there with the same 2 adjacencies they will get 4 science)
If your Blacksmith has 2 adjacencies then a specialist placed there gets 2 science 2 culture and 1 production.... if it has 4 adjacencies I get 2 production
So if I want to specialize my city, I do it by Where I put my specialists. (if every tile is filled to the max with specialists and I have every possible building...then I am going to have a generic city (maybe specialized based on which buildings have the best adjacencies.)