Staining should be done before the filler, since filler makes even penetration of the stain more difficult. (Been there, done that.) An initial seal coat keeps the filler from staining the base wood, and colors only the pores. So--first use dye to get the base color right, seal it with dewaxed shellac, and then apply the filler. The filler should be colored so that the pores end up the color you want. To keep them light, use the Behlen's natural and add just enough oil paint to get the right shade. This will give you pores anywhere from cream colored to dark if you add lots of pigment. Good colors are yellow ochre (earthy yellow), burnt umber (basic brown) and burnt sienna (reddish brown.) Then let the filler cure really well--the overnight recommendation on the label seems awfully short--I'd wait at least 48 hours before applying a top coat.
You do have to experiment on scrap of the same wood--this kind of multi-step finishing schedule makes it very important.