Just as the title says, should the MPS innner screw change the idle mixture?

I keep on reading about the idle circuit triggered by the TPS position which switches mixture control over to the ECU knob.

Both the MPS and ECU knob change my idle mixture, the bigger control being the MPS. Is that correct function?

The inner screw changes the AFR everywhere. If the AFR is set correctly then the idle mix is close and can be fine tuned with the ECU knob

I'm not sure you should think of the MPS "setting at idle." There really isn't one. When tuning the MPS you're creating a slope (like a line on a graph) of enrichment, starting from high manifold pressure (which corresponds to idle in most driving situations) to low pressure (cruising) to no manifold pressure (WOT).

The ECU knob is supposed to have a minor effect on mixture (each click is minor) and is independent of MPS adjustment. In other words, the effect is cumulative.