Your 'buds' are probably cones. What is wrong with it, if anything, it is impossible to say with this amount of information. Perhaps the other one will start coning soon as well. Otherwise, it is true that stressed arborvitaes (and other conifers) may cone heavily in response.
I too have a question about globe cedars, I planted 4 globe cedars in the Edmonton area (zone 3) in a south facing yard about 5 ft. between each one in a row. They were relatively small (approx 3 ft. tall) when I planted them and were completely covered by snow through the winter. 3 of them came through great but the last one is yellow colour on the outside but still green in the inside, it is defintely alive still. Each cedar gets equal amount of water (from snow and sprinkler system), sunlight and all-purpose fertilizer but the last one is on a 20 degree or so slope. Is the slope enough to cause my problem. Any suggestion as to what my problem may be and what I can do to fix it.