I went through a similar situation with my house after a tornado hit it. I had the actual replacement cost rider on my house. This is how it worked for me.
The insurance adjuster came in to determine the loss. He depreciated the loss to 50%. He cut me a check for that amount. Then it was up to me to get the repairs done. I hired a contractor to make the repairs. Once the repairs were done and I was billed, the insurance company reimbursed the difference. Since there were more homes in my area that got hit by the tornado, I had to wait in line for 6 months for work to be done. A very eye opening experience for me. Chuck B.