The key to filling holes in stain grade wood is to only get the putty in the hole. When you putty bare wood with a putty knife, it gets putty in all the little grain pores around the hole. Striking the surface smooth with the putty knife forces it into all the pores completely. You really won't notice this until you apply the clear finish. It makes all the putty shine. From a distance it looks like what you describe. Look closer and you'll see that it is really just filling the pores.

One way to correct it at this point is to use a toner over the finish.

Another way is to select the colored putty wax pencils, carefully scratch out the putty from the pores, and touch up the surface with wax pencils.

I always put clear finish before putty. The first coat of finish is called the seal coat. This fills all the pores with clear finish. Also known as "sanding sealer," once you sand it smooth and add another coat of finish, the surface pores will be completely filled and the wood will be smooth as glass. If you're using solvent putty, now is the time. Put it on after the seal coats, but before the top coats. If you're using colored wax pencils as filler, complete the top coats and let them cure properly before filling the holes with wax. Buff the surface with a bed sheet rag to remove the wax residue.