I am not sure how did you rotate the polygon grid, but it seems you have used Rotate tool from Processing toolbox. If so, you need to specify the Rotation anchor [x,y], which enables you to select the rotation position directly from the map canvas, as you can see below:
Using Rotate tool:
The Rotation anchor [x,y] was selected at the center of the intersection of the 4 polygons:
Alternatively, you can use the edit button to start editing, then select all polygons using the selection tool, and finally use the rotate tool to rotate the polygons
But be careful, if you choose the alternative approach make sure to work on a copy of the polygon grid because once you save the edit it is irreversible.