We had a nursery plant 15 arborvitae trees in May 2003. We mulched them and then watered them about once a month or less or more depending on rainfall. A number of the branches turned a rusty color. Eventually 6 of the trees died. The nursery replaced them this past spring and the same thing has happened.
The damage you described can be a result of transplant stress or disease. Proper watering is the key to establishing a healthy tree. Water the rootball and beyond the planting hole whenever the top 3 to 4 inches of soil is crumbly and slightly moist. Wet the top 8 to 12 inches or soil. This is usually provided with an inch of water applied once every 7 to 10 days in clay soil and in two applications (1/2 inch each) per week in sandy soils. Adjust your watering based on the temperature and rainfall. Use the soil moisture not your calendar as a guide. Branch dieback can be the result of twig blights caused by a fungal disease. Small black dots (part of the fungus) can often be found on diseased branches. Ask your nursery to check for signs of disease. Twig blights can usually be controlled with proper care and pruning. Remove infected branches and disinfect tools between cuts. Avoid water on the leaves, mulch the soil around the plant and allow the plants to get established before you fertilize.