Yes, compost / organic matter will absolutely help, especially if topsoil is clay heavy. Grass clippings and shredded leaves no matter how decomposed they are will work.
Any compost / organic matter you can add to the mix will benefit the new sod. Tilling top soil in is a good idea, especially if you've added in compost! Seems like contractor is tilling (absolutely good) & compacting (good to an extent) new top soil. Highly unlikely contractor is over compacting new top soil - you want it flat for the most part.I got a look at what I thought was a tiller. From a distance it had looked like it was churning it up like a tiller & leaving it flat. It has a knobby cylinder that rotates. It looks like it will pulverize clods & level the soil. It brought a lot gravel to the surface. It also seemed to pack the soil.
If I can get organic matter out should the device do any good? I have a tiller & could take advantage of them breaking clods, etc. Then I could spread stuff & till it in. Does the soil need to be packed to lay sod? My logic says not too packed, but I defer to you pros & your experience.
Should I rake off the gravel?
What's the ideal thing to add in? I think the years of compost I have is pretty good, but I know some plants don't like some kinds of compost-like azaleas don't like oak & sweetgum leaves but do like pine straw. Also, I might not have time to collect it. If I have to buy something I want to choose right.
Thanks for advice.
Don't forget I'll be glad to share from my experience if you need to hang stuff on the wall.