This setup should work:
How it works step by step:
Reset position of vertices by subtracting their median position. So that points are in center of coordinates and you can easily do the next steps:
Scale vertices by multiplying by empty's scale.
Rotate vertices like you did, but around center of coordinates (0,0,0)
Move vertices by difference between empty and median position of points.
Now undo the first step to get points back, with transforms applied