Stabilizer/final rinse foams quite a bit. If it bothers you, it's recommended to do that step outside the processor. But if you have only 250 ml of solution, it's not possible then. But, I use the processor for stabilizer/final rinse too every now and then, and foaming hasn't caused any problems.
BUT. When I stabilize with the tank attached to the Jobo, I don't use the lift system at all. I remove the tank, carefully pour the stabilizer in the tank and then attach the tank back to the processor. And when the time is up, I remove the tank from processor. This way, I don't have to wash the processor funnel system afterwards, as it gets washed simultaneously with final wash of the film. If you let stabilizer touch with processor's funnel system, you have to wash it out.