100% it will bleed. You will need to try to find a translucent pigment to use instead of the dye to make it non bleed, not always possible but if you can it will help greatly.
I cut my lip slot on my bandsaw, while my blank is still rectangular, so it's square to the blank
I mark a centerline on my lip and on my finished blank, so I can line them up when I glue them together.