It's slightly different depending on the type of control goal:
- If it is "Control [civilisation]", e.g. in the Greek or Prussian goals, it always refers to their core area. If the civilisation is dead, one city in the core is enough. If they are still alive, you need two cities, and more than they do. Cities owned by your vassals only count as yours if it is explicitly mentioned.
- If it is "Control [geographic area]", e.g. in the Iranian and Tamil goals, you need at least one city in the area, and no other major civ may control cities in the area (i.e. independents are allowed).
- Turkey is special again, in two different ways: for the cities, you need to control the city on the designated tile, or one on a directly adjacent tile (in case cities are arranged differently that expected). For the areas, you need to culturally control all mentioned tiles.
- If it is "Control [civilisation]", e.g. in the Greek or Prussian goals, it always refers to their core area. If the civilisation is dead, one city in the core is enough. If they are still alive, you need two cities, and more than they do. Cities owned by your vassals only count as yours if it is explicitly mentioned.
- If it is "Control [geographic area]", e.g. in the Iranian and Tamil goals, you need at least one city in the area, and no other major civ may control cities in the area (i.e. independents are allowed).
- Turkey is special again, in two different ways: for the cities, you need to control the city on the designated tile, or one on a directly adjacent tile (in case cities are arranged differently that expected). For the areas, you need to culturally control all mentioned tiles.