Any compost will do as long as it's been sterilized. Compost will disappear over time. Topsoil won't.

Compost, by definition, is not sterilized. It is just the opposite. It has bazillions of bacteria, fungi, protozoa, and micro-arthropods to replenish any you might have lost due to soil sterilization, poisoning, disease, or other tragedies. If you do something like steam sterilize compost, you may as well have bought cheap peat moss.

I disagree with using any topdressing when seeding. The worst thing that can happen is you bury the seeds that are supposed to be on the surface. Then they won't germinate. The best thing that can happen is the compost helps to hold more moisture against the seed for longer so the seed germinates. Whether you use compost or not, you should still roll the seed down with a roller. Once you opt for the roller, then the topdressing is superfluous.

Only use real topsoil if you already have a drainage problem you need to correct. Why? Because topsoil is definitely going to change your drainage.

Back to your specific compost, I wonder why they would need to screen a compost made from the ingredients mentioned. Nothing in that mix is larger than 5/8 inch to begin with - at least not after 18 months. Maybe they have wood chips in with the saw dust. That sounds like reasonable compost. The more original feed stuffs you can get the better. For example it would be better compost if they had restaurant scraps, food manufacturer waste, grass clippings, tree trimmings, brewery waste, etc.

When talking about compost, sterilized doesn't mean it's bacteria free. It means it doesn't have viable weed seeds. If the compost is heated to say 140F for a period of time, it will kill all the weed seeds. This can happen naturally in the middle of a compost pile if the pile is sufficiently large.

Large seeds, like grass seed, germinate much better if covered. Small seeds need sunlight to germinate. I'm sure there are exceptions, but, in general, this is how nature works. It's typically recommened to cover grass seed with 1/8-1/4" of soil. Sometimes people cover with straw. I don't recommend straw as it doesn't work as well and can have weed seeds in it. If you can't do this, rake the seed in by scraping the top surface of the ground.