Yes, the coils do touch when stationary.
I think the softer part just acts a bit like a helper spring that you get in some front coilovers, keeping the spring (which is now shorter than a standard one) in place when the travel is at full droop.

I have read that toe-out improves steering response, but too much will scrub the tyres on the inside so you have to have a compromise.
I guess you could ask them to give it some more toe-out to see if it helps, at the risk of your tyres wearing quicker.... or you could have a play by turning the track rod ends a couple of turns on both sides
I remember when I first got my ST and the tracking was well out, the car was very darty.

Car looks really nice!