The stain should be applied after carving.
I coat the entire carving with a sealer or wipe-on poly after carving. Then add dark stain or paint. Wipe or sand off what sits on the original surface. What remains in the cut surfaces will appear darker, the wider the cut.
Or, if you omit the sealer, note that the cut areas expose end grain, which absorb more stain than than the surface will. Of course for this to happen, the raster angle needs to be at an angle to the grain. 45 degrees works well.
Good judgement comes from experience.
Experience comes from bad judgement.