Call your landscaper now and cancel this project. It is totally unprofessional and irresponsible to be seeding a new lawn in the summertime. You need a new landscaper.

Where do you live? There might be an exception to this if you live on the Pacific coast or New England coast. But those would not be zone 5. Need to know where you live.

The problem is the new grass plants cannot withstand the heat and dryness of the summer. They will die out leaving room for weeds. The other problem is that crabgrass is germinating right now. If you water your grass seed like you are supposed to, the faster germinating crabgrass will come in like a wild fire to choke out your new grass literally before it gets started. By the end of July you would likely have a majority of crabgrass in the lawn.

Now is an okay time for new SOD, but not new seed.

And to answer your original question (since you are going to have it seeded anyway) the use of straw is only practiced in a few parts of the country. The rest of the world scatters compost or mulch. I don't like either of those approaches. Those trying to do it more naturally will use a water roller to roll the seed down. This makes good contact between the seed and soil, and that is the point of the other approaches. As you already know, straw or straw mat just adds profit to the job. It also brings in other issues that you don't need to bother with if you do it the more natural way.