How do Expansions work in the Settlement?
Expansions work a little differently to the main game. For one, all expansions can be placed at any time, as long as you have the cultural goods or diamonds required. However, once you finish or abandon the settlement, all Expansions will be removed, including those purchased with Diamonds.
To buy the expansion, make sure you have one of the required goods (you don't need all) and select it by clicking it. If you have the goods required, the button will be shown with an orange highlight.
In the Viking Cultural Outpost, Viking expansions can be purchased with cultural goods or Diamonds. You can select what cultural good you would like to pay for any expansion and only one of the goods is needed per expansion.