That will happen with any wetting of the wood surface.....depends if you intend to put more dye onto it, or find it dark enough.
Wait till you get that correct, then swab off parts you deem too dark as best you can before it dries.
You want to wet / dry swab out, dye as best you can to get the colour you want...... If you have a veneer top, you only have .5mm of veneer to work with, so sanding is NOT what you want to be doing to adjust colour.
You also have the problem of possibly over saturating the veneer, making it lift...so be careful..... it's a fine line between whatever you choose to do.
A solid top like yours..... well you have a lot of latitude , and very little can actually mess up to such a stage that you need to think of a total refinish.