After seeing how Madoka instantly transformed into her witch form after killing Walpurgisnacht in one shot in the 4th timeline, it makes me wondering: How do Soul Gems become corrupted?
I assumed that over time the magical girls would lose hope and fall into despair, which then clouded their Soul Gems. However, Madoka instantly turned into a witch, without any real reason to despair.
Soul Gems do indeed gradually darken over time, even if a magical girl doesn't do anything magical. I'd imagine this is because the gem still needs to magically sustain her body, or something like that. But they also darken for other reasons - the emotion of despair causes a Soul Gem to darken, and so does the use of magical powers.
In the 4th timeline, after defeating the Walpurgisnacht, Madoka had no reason to despair... but she did expend an enormous amount of energy to defeat the Walpurgisnacht in one shot. Apparently, that was enough to cause her Soul Gem to blacken completely, thus resulting in her becoming Kriemhild Gretchen.
I'm assuming you meant how Soul Gems gets corrupted over time. Grief Seeds don't fill up after a Soul Gem is destroyed. In fact, they only exist after a Soul Gem is destroyed. A Puella Magi does not have a Grief Seed, they only have a Soul Gem. Soul Gems gets corrupted after its owner uses their magical powers.
As for why Madoka became a witch immediately after making her wish in the most recent timeline, it is because the miracle she wants out of her wish is simply too great. It requires a great amount of magical powers to fulfill as she needed to change nature itself. Thus her soul gem became spent and she became a witch.
So we know that Grief Seeds are former Soul Gems that became too polluted. (This can be confirmed in Wikia-type sources such as here.) So the question is also about how easily Soul Gems can become polluted. As it seems, there are several ways for this to happen:
Despair and pain. This I believe happens with Sayaka and is shown to us in episode 8.
Normal use of magical abilities:
This is why Mami's Soul Gem becomes slightly polluted, and why in what should be the second episode, she shows Sayaka and Madoka her use of a Grief Seed she collected to clear it up.
Notably, we also see Homura use her Soul Gem to improve her eyesight and get rid of her glasses, when she decides to take more drastic action to save Madoka -- so in some sense, maybe the Soul Gem contains some sort of energy or vitality.
In the case of Madoka in the timeline you mentioned, the second scenario seems more likely, due to the amount of energy that would be required to destroy a witch so easily.
adding onto another answer -- they mentioned on how Madoka's soul gem blackened instantly due to the amount of power used to defeat Walpurgisnacht. earlier in the show we learn about this. Mami mentions how her soul gem looks duller than last time, because she used some power in one of her battles. She mentions how they have to be cleansed / purified after use, otherwise they'll go dark. because of this logic, that's how madoka's soul gem instantly blackened. the power she used was so great that it took everything out of the soul gem.
