That’s okay, nobody should take Starkiller particularly seriously. Not that it matters, but Starkiller’s reverse grip is supposed to be a variant of the Shien lightsaber form. Which is a polite way of saying, “he’s probably doing it wrong.”
If you’ve never looked at Star Wars’ extended universe, there’s supposed to be seven different lightsaber forms, all with Asian sounding names. And then everything falls apart, because there’s actually nine different forms, and they’re numbered I-VII. Shien is the second Form V (or the first), and if it sounds like I’m about to gnaw my own arm off to escape, I am.
There is absolutely no reason to wield a sword in a reverse grip except in trying to say, “I look like a badass,” and actually saying, “I have no idea what I’m doing.”
However, you will find people holding knives in reverse grips for any number of reasons.
The biggest advantage from holding a dagger in a reverse grip is concealment. You can have the knife out, ready to use, but still hide its outline against your arm. This makes it harder to see, and more difficult to defend against. Which is the reason you’ll frequently see assassins and rogues depicted holding their blades like this.
Reverse grips are somewhat inferior for parrying incoming armed attacks, but they can also do very nasty things to an unarmed opponent who tries to parry incoming knife strikes. Generally speaking, a reverse grip makes the knife slightly harder to deal with.
A reverse gripped knife can also be used to augment some unarmed styles. This is really a case-by-case option, but for certain kinds of punches, a dagger will simply add an extra laceration to the strikes.
This also allows you to “two hand” a knife or dagger, by applying additional force with the off hand to the hilt, and driving the blade with both arms. There aren’t a lot of applications for this, but if the situation calls for it, the results are dramatic.
It’s also worth pointing out, because knives are so light, it’s very easy for a practiced knife fighter to switch their grip mid combat. When you hear characters talking about the balance of a knife, this is one of the reasons that’s an important consideration. A knife that’s not balanced to the fighter’s tastes will take longer to adjust in combat.