I've had the something happen, some times it will even out, but most of the time it does not.
Here is how I fixed this problem;
1. Dip dye very quickly, do not let the leather sit in the dye for more than a second or 2.
2. Dip dye before you put holes in your project. This is very important, because dye will follow the path of least resistance, allowing more dye to saturate the leather where the holes are, just like it did on your edges.
3. If all else fails -- dye it black.
Good luck.