UPDATE: They did the checkup last Thursday and everything was fine with the fluid, so they just recalibrated the "brains" controlling the gearbox. The half an hour drive back home from the service was fantastic, it felt like a different car, no jerking whatsoever, smooth switching and so on, but maybe it was a placebo effect or something, because the next morning the occasional jerking returned, although nowhere as "donkey-style" as before.
I've been watching the gearbox behavior closely these days and it's safe to say that overall the recalibration helped, having reduced the kicking considerably. It still happens sometimes, but it's barely noticeable and doesn't create much of a driving discomfort.