Quick note on airbrushing with ANY type of oil. Use a respirator because oils, when atomized, can cause lung issues.
When I dye it's oil, dye, buff, finish.
I oil with neatsfoot oil and let it sit until the oil is absorbed. How long it sits depends on the thickness of the leather. This allows the dye to spread evenly when applied.
I then dye and let it sit for a day so the dye has time to spread evenly.
I then buff any excess dye off.
I then add my finish, usually Resolene diluted with water 50/50 or a wax.