Do these projected tracks assume existing atmospheric conditions, or what they expect the conditions to be in the future?
They are based on averaging of several different model runs. The models attempt to initialize the storm as to what the position, strength and environmental conditions are and then move it out into the future factoring in water temps, landmasses and other weather patterns - hurricanes almost always react to steering patterns instead of causing them (some really strong ones can affect their own steering patterns).
I don't know how much of a model is pure math and how much is based on factoring in history. But if the model can't properly initialize the storm, it can be problematic to forecast it. And it's just a guess, but I think the forecasters are getting a bit too dependent upon the models instead of looking at the current live data around the system (that initialization thingy).