I have used two methods that come to mind. Either put a finish on the wood to seal it, then carve your design leaving porous wood to receive your finish.
This could be a dye or it could be a powder that would become permanent when the finish, or another was applied. Powders could be pigments or things like coffee, ground inner Birch bark or even rust.
Dyes vary depending on the finish. Traditionally a water based dye might be applied if a oil or spirit based finish was used, and a spirit based dye before a water based finished . Experiment because now these rules can be broken,
An alternative is to carve then seal where you do not want a dye to penetrate. A common sealant for this method would be Shellac, but anything that would block the colour would work. ( Oil, Wax, Varnish etc)
As you are chip carving I would suggest the first approach. Seal the wood, then carve your design before dying, staining or adding pigment. If though, you want to stain the item and leave where you carve a natural colour, then experiment and see how far the stain penetrates. You might want to try colouring the finish to stop it going to deep. Sanding sealer ( both spirit and water based) will recieve a stain, but can stop it going to deep, especially if you use the opposite type to your finish.
Wood, even from the same species varies, so it is always best to experiment on scrap first. If end grain is part of the design, such as in a bowl or cup. You might want to apply a finish after carving and before staining. If you don't , you might find that the end grain will absorb more stain and become darker than the rest. This might though be a design feature you can play with, adding shading or such.
Good luck, I look forward to seeing what you make,
John
