Good to see you have moved on from mission impossible.....Korina finish as that requires a light coloured timber where mahogany has too much pink and brown hues to contend with. Cherry should work a lot easier.

The filler looks like it could be similar to Timbermate that we find in hardware stores over here. The one in that picture is natural which would come out looking almost white, which is.....natural afterall as you want it to soak up the colour of stain being applied.

Suggest re-applying the grain filler and leave it to dry and harden up for 48 hours and then lightly sand off with 180 or 240 grit. You could maybe add some stain to the filler to colour it which assists in blending in when stain coats are added.

To get better depth of colour you may need to add a few stain coats until it arrives at desired colour.