I hired a landscaper to spread 30 yards of top soil prior to laying sod. He insisted on dragging his bobcat scoop across the soil to give it a nice compaction. It seems to have worked well in all areas other than the side yard where most of the landscaping traffic was(including concrete bobcat and loader traffic). He laid 4" of soil on the side yard towards the end but because of all this traffic it is just rock hard. It has been really dry since this was laid, which doesn't help.
The problem with compaction by vehicle is that it can easily destroy the ability of the soil to drain well. It also makes it more difficult for any plant's roots to move through the soil as they normally wood because it destroys the pore structure of the soil; it also reduces the ability of the soil to hold water. Your "landscaper" (using the term VERY loosely) does not seem to know his trade. If he ran the bobcat over tree roots he actually damaged the tree.
If your land slopes towards a neighbor's house, and if the landscaper damaged the soil bad enough, any heavy rain will run off onto the neighbor's land and possibly into their house. Saw it happen about 2 blocks from my own house. He needs to replace at least the top six inches (top foot would be better) of the soil he laid in the heavily trafficked area and then PROPERLY compact it. Tell him to leave the damn bobcat on the trailer after it removes your soi- er, brown cement. This will more than likely leave you with hardpan under good soil, but the drainage should be much improved.
Soil type is going to be a major consideration. The finer the soil, the harder it will be to use a tiller. You may be able to scuff up the top layer of soil to an inch or two but likely in the hard area not much past that. One of the issues is penetration by water to get to deep layers to ensure that grass will survive. Even in an agricultural context it is often necessary to run a plow to open up the ground before trying to use a tiller. Tillers are more for frequently worked soil with high organic matter.
An alternate approach would be with a broadfork. Broadforks are designed to penetrate very deeply and force a channel from surface to about 10 inches down. They come in various sizes and heavy duty weights for treatment of hard pan, and leave the layers of soil pretty much intact, where a tiller would mix everything up. So they are appropriate if you have good soil on top and want to leave it there, but dramatically improve drainage and relieve compaction. They are often available at rental outlets.