It sounds to me like they may not be getting enough water. I usually water 1 or 2 times a day for new plantings, and rain isn't going to take the place of watering unless it rains pretty heavily. Make sure that you're getting the water deep enough to get to the roots, a slow trickle with the hose can be the most effective. It has been hotter than usual, which puts added stress on freshly planted things. I would make sure the roots are staying moist and give it a little more time.

A planting hole filled with black dirt surrounded by clay soil is like a creating a bowl of water in the ground. Arborvitae do fine in clay. Next time you might want to mix a little black dirt with the clay so there's not such an abrupt change in soil texture.

Could be they're getting too much water. No criticism intended to anyone--most people tend to overwater rather than underwater.

What condition were the roots in when you planted them? Also consider how close the exposure direction matches the plant's cultural requirements. Too much intense, hot sun might be the problem as well as too low a soil pH.

BTW, current recommendations for planting are for wide and only as deep as needed to accommodate the roots.

Here is a link that might be useful: Planting and Transplanting Trees and Shrubs

Original Poster here:
So my arborvitae basically turned all brown except for the very center of each plant. I decided to try and give my arborvitae a "haircut" and trim off all of the brown foliage. Well, I did this to one of the plants, not sure if it was a smart move or not, what are your thoughts?

By the way, i think i was under-watering the plant which is why it started to die in the first place.