This may have happened to you. It’s surely happened to me. When you’re brushing a finish, the brush picks up some of the stain and lightens the wood. It’s even worse when the brush picks up so much stain that it leaves streaks.
The first solution to try is to let the stain dry longer. Oil stains usually require drying overnight in a warm room, longer if the room isn’t warm. Water-based stains dry much quicker, but the drying can still be slowed by high humidity and cold conditions.
If drying for a longer time doesn’t solve the problem, it could be that the stain just doesn’t have enough binder in it to fully glue the pigment to the wood. So seal the stain in the wood by spraying the first coat of finish. If you don’t have a spray gun, use an aerosol.