Are you sure you are not talking mineral spots in the actual wood? Your cabinets should be finished with a catalyzed varnish on the exterior that would not allow coffee or oil or anything else to penetrate into the wood and that can be easily cleaned with a bit of detergent and a microfiber cloth.

No, these are definitely splatters, not the natural dark markings in the wood.

Any spatters should be on top of the finish.

Soap and possibly very mild abrasives (think toothpaste).