Dude.

First off, it's purely a hypothetical model. You can plop in negative time to equations and have them make sense, this doesn't mean that negative time is possible.

However disregarding that. The abstract of the study:

We study the internal dynamics of a hypothetical spaceship traveling on a close timelike curve in an axially symmetric Universe. We choose the curve so that the generator of evolution in proper time is the angular momentum. Using Wigner's theorem, we prove that the energy levels internal to the spaceship must undergo spontaneous discretization. The level separation turns out to be finely tuned so that, after completing a roundtrip of the curve, all systems are back to their initial state. This implies, for example, that the memories of an observer inside the spaceship are necessarily erased by the end of the journey. More in general, if there is an increase in entropy, a Poincaré cycle will eventually reverse it by the end of the loop, forcing entropy to decrease back to its initial value. We show that such decrease in entropy is in agreement with the eigenstate thermalization hypothesis. The non-existence of time-travel paradoxes follows as a rigorous corollary of our analysis.

So the study the article is based on concludes that time-travel paradoxes are impossible. Thus you can not kill your own grandfather because it'd create a paradox. What they're saying is that you could be in a CTC (closed time-like curve) where in which time goes back and forth from your grandparents to you and back again, but the time going back would reduced entropy ie reverse things.

So you couldn't "go back" because that'd mean your entropy ie your arrow of time, was still pointing forwards and not backwards.

This isn't a case of some random Lemming against a professor saying otherwise. It's Lemmings telling you you've bought into pop-science sensationalism.

The article does actually communicate what I explained there, but really almost hides it with the language, so I'm not surprised your either didn't read it, missed it, or didn't internalise it:

Circling back to a spry young grandfather courting your grandmother the first time, the time loop could make his untimely death reversible; your memory of why you ever wanted to murder him in the first place may be erasable. In other words, all bets are off in a closed loop where quantum physics smoothes out any intrusive entropy.

Ie nothing here is breaking the Novikov self-consistency principle