One controller, two LED strips (one white, one RGB)

I’m in the planning stage of building a frame with light(s).

The idea I have is to attach the white LED strip inside the frame and the RGB strip behind the frame and hang it on the wall with a small distance to the wall so that the light shines out like this (yellow is represents the white LED)

The issue is that I’m hoping to use one controller and one power supply to make it easy to work with (on/off, color change).

I have had good results with Sonoff L1 in the past so I’m leaning towards that for the RBG.
I just want to make sure what I’m thinking is correct and I’m missing something.

The Sonoff is connected to mains with a power supply delivering 12 V.
Cable goes controller.
Controller has four wires out 12v, and three grounds.

What I’m thinking is the following:

The RGB strip is working since that is a off the shelf product.
And in my mind the white strip gets 12 volt from the controller when the RGB is on but because I ground it before the controller it should get a clean ground and not be dependent on what color the RGB is displaying.
If I had connected the white ground to the same ground as the RGBs then it would dim or be dependent on the color it’s connected to.

Is my thinking correct or have I missed something?