By saying their arrows are spined uniformly, they are saying that within a specified range of weights, their arrows will resist flexing to the same degree all around the shaft. BUT- this does not mean that the arrow won't have a slightly stronger or weaker side (within the tolearances of their weight measurement range). Even aluminum arrows all have a spine as we are describing it here. They tend to have a less pronounced spine than carbon arrows, but it's still there.

The bottom line is always how your arrows shoot. If all of your arrows group well, you don't need to worry about any of this. But these things explain why some arrows are "off" of others, and they can help tighten arrow groups for experienced shooters. For hunting stuff, these slight adjustments rarely matter.

You ask what the advantages of carbon are, I'll say it again. For me, it boils down to two things.
1) once straight, always straight
2) stronger than aluminum (for any given weight of arrow), allowing you to use a lighter arrow and gaining arrow speed OR giving you a stronger, tougher arrow of the same weight.