It sounds like you removed the trees, is that correct?
TifTuf was very easy to establish for me. 100% of the pieces of sod took hold without any hiccups. For initial success just add lots of water and sunlight.
Not sure if you had Bermuda in this area before now, but if you did, make sure it's all been killed off 100%. Even Tifway creeping into a TifTuf lawn will be noticeable to the keen observer. A well fed Tifway is a little darker than TifTuf.
A soil test is a really good idea. If you can lay down any needed phosphorus and potassium, I think it's best to get those nutrients in the soil first so the roots can find them.
And you can cut it whenever it's growing. As long as the sod comes cut relatively short you're not going to hurt it. Just don't cut too much leaf off at first.
Rolling helps some, I would recommend it. But it will be uneven until you can sand level the lawn. The sod pieces are cut in varying thickness. Surprisingly varied, I found.