Information can’t travel faster than light, things can.
The experiment, which is remarkable for how precise and clean it was in only involving a single particle in a single, bound system, simply shows that there’s no fundamental quantum delay in this tunneling transition.
But it also helps expose how we have managed to exploit a many-particle system in order to create an illusion of something traveling faster than the speed of light: a result which gets misreported every few years in the popular media.
Imagine you’ve got a set of quantum particles, bunched together into a tight pulse, tunneling or otherwise traveling through a barrier of some sort.
It’s truly remarkable how successful we’ve become at imaging pulses that move at speeds that approach or even equal the speed of light; thanks to novel techniques and technologies.
What you can do is, measure where this pulse is located in space at a certain instant in time, before it encounters a barrier, where and when you expect that pulse to arrive if it were to travel at speed of light and successfully tunnel through the barrier.
And then comparing your measurement for where the pulse is located in space at a later instant in time, after successfully tunneling through the barrier.
It might surprise one to learn that the pulse we detect on the other side of the barrier can easily be found appearing to move faster than the speed of light would seem to permit.