Was just having the same issue and came on here to see if anyone has an answer. I have found one way I think might work.
Under the expressions tab, in your expression , you need to add an 'IF' statement into the Background Colour category. A simple If(Dimension ='xxx',RGB(0,128,0),If(Dimension ='yyy', RGB(256,0,0))) etc should solve this.
It is a bit long, but is the only way I have been able to get arounf this.
Anyone know any other method of doing this?