Incorporating topsoil

I'm working on a complete re-work of my front yard - converting a sloped lawn to a terraced lawn.
Now that the grading is done, I'm left with a flat surface with no topsoil at all. I'm awaiting the results of a real soil test, but I already know that the current dirt is not suitable for growing anything. (The glass jar/soapy water test suggests 80% sand, 15% silt, 5% clay.)

My plan is to bring in 4" of "blended garden soil" to support Zoysia sod. My question is about incorporating this topsoil into the existing fill. I've read several things suggesting that tilling 6" is good general prep for sod. So does this mean that I should add my 4" of topsoil and then till it and the first 2" of fill together?
Am I approaching all of this the right way, or am I completely off base?

Thanks