Why Is My Tile Spacing Uneven?

This boils down to the tile setter's inexperience. The tile is irregular so using a 1/16" spacer is going to cause problems quickly. Before you know it you a have what you see in this picture, inconstant grout lines. These tile should be set manually by eye. Also a tile like this requites a larger grout line to keep the pattern looking uniform. An experienced tile installer eyeball the spacing while stepping back from the wall every so often to be sure he is keeping his lines strait. This homeowner asked if the tile will look better once grouted

This homeowner asked if the tile will look better once grouted. I can say with 100% certainty it will only get worse. Grout usually makes the joint spacing irregularity more visible. See the image below.