In order to get dynamic coordinate columns, you need to use column formulas. To do this:
- Select the layer in the Layer Stack
- Use Window > Show Layer Info if it isn't already showing
- Choose the Fields tab if it isn't already showing
- Locate or add a column to store the information in
- Make sure the column has a type of Float
- Select the column name in the list and click Set Formula...
- In the formula area enter "geometry.centroid().x" for the x column and "geometry.centroid().y" for the y column
- Click OK
NOTE: this will use the map coordinate system to compute the coordinates. To use the layer's original coordinate system use "geometry.centroid(1).x" and "geometry.centroid(1).y" respectively for the x and y columns.