Thank you for your help!

If he is indeed a licensed landscaper then go with him..I say.

The raising of the ground was I suppose before any turf was grown. You didn't say just how much it was raised...surely not the 6" that you say you sink after stepping on the grass that has grown.

If that is the case, then yes, surely you have to roll it, compress it to some degree....but definitely not to a point that the ground is now compacted.

The grass will use the depth of good soil to firmly put down roots...but they shouldn't be floating. The rolling should take care of that.

Fertilizer used to hasten and feed a new lawn in the fall is now commonly done. Most of the 'experts'...the people who know grass, say putting a starter fertilizer down when seeding is a good idea. The fertilizer feeds the soil, improves the chance the grass will grow sturdy.
There is some question as to the degree of nitrogen such fertilizer contains.
Me, I'd trust the bag's directions; if it says its a starter type fertilizer, then by all means use it with confidence.

Such feeding in fall is said to be better put down at this time...and the need for feeding in the spring is lessened.
That is the idea...whether it works out that way is another matter. Winter takes an awful lot out of a lawn and feeding a high nitrogen lawn fertilizer speeds up greening, accelerates the filling in of bare patches and gets the lawn off to a good start.
But, it shouldn't be the only feeding....a three-time, minimum, feeding program should be given a lawn to keep it healthy, increase the growth potential and builds the soil to produce a tough turf.

This feeding of nitrogen based fertilizer can be helped with the adding of top layering of a good thriple mix or compost to help the soil take in organic matter which helps retain moisture and feeds the soil micro-organisms.

That means you did not pay for it or specify it in your RFQ. Contractors bid on minimum requirements unless you specify otherwise. You basically got what you asked for.

And to texas-weed, we paid generously for a job well done. Nobody would hire somebody who is just willing to do the very minimum, not care about the outcome and be dishonest.

New grass is almost always fertilized before cutting. Texas Weed can comment on that since he's recently retired from the sod farming business. And what would be the point of fertilizing bare soil? There are no roots to take up the fertilizer.

The idea of rolling is not to compact the soil. There is a tool called a sheep's foot for doing that. And the sheep's foot is used to settle the soil, not compact it. It takes it from fluffy to relatively settled but without any specific soil structure. So the idea of rolling the new sod down is to ensure you have good contact between the soil and the new sod. Grass roots will not grow through the air to reach the soil. They must be in contact with moist soil.

The gurus I trust say to apply half the starter fert on the new grass and half in a few weeks (after mowing).

Sounds like your contractor is losing money and using all the tricks to try not to lose much more.