Those cracks probably aren't from the mineral oil itself, more likely they were already in the wood and are just opening up as the handle moves around. Dark hardwoods like ebony or dyed wood often show this, especially if the piece dried out in a shop or moved to a drier climate in your house. Wood expands and contracts with humidity and small checks along the edge of the handle are pretty common on handmade knives.
The bigger issue is that mineral oil never actually cures. It just sits in the wood, so it conditions it but doesn't seal it. That means the handle keeps soaking up oil and giving off moisture, which can make existing cracks more visible and keep them creeping. Oil helps keep the wood from drying out further but it won't stop movement on its own.
If the cracks are still hairline, a couple drops of thin superglue wicked into them will fill and stabilize them, then you can level it with fine sandpaper and the repair basically disappears. Lots of makers do exactly that. Once that's done, give the whole handle a light sanding to knock down any rough spots. For a real finish, you want something that cures hard instead of staying oily. Tung oil or boiled linseed oil are the usual choices for wood handles, applied in thin coats and wiped off, with a few days between coats. Some folks finish with a coat of wax on top. That gives you a sealed surface that won't keep drinking oil forever. Just skip anything with a thick film like polyurethane if you plan to actually use the knife, since it can chip around the pins.
Also worth a message to the guy who made it. A smith with two decades of experience will know exactly what wood he used and how it was sealed before it left the shop, and most are happy to touch up a handle for you.