Certified GKH Gardening Expert
This appears to be a fungal infection. This can happen when the season is overly wet, or from over irrigation.
You will likely have to remove the trees heavily affected, as they will never fully recover. I would treat the area with a fungicide as well, before planting. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
This article will help you to care for Arborvitae: https://www.gardeningknowhow.com/ornamental/trees/arborvitae/growing-arborvitae-trees.htm