This article is not about classical negative mass or exotic matter – which would be major breakthroughs.
https://en.wikipedia.org/wiki/Negative_mass
It is about "engineering" of the dispersion relation – wave-related phenomena that can have counter-intuitive effects at small scales where multiple waves interfere:
https://en.wikipedia.org/wiki/Dispersion_relation
In this case, the "counter-intuitive" effect is that the particles appear to move the wrong way when subjected to forces, resulting in an "effective mass" with a negative sign:
https://en.wikipedia.org/wiki/Effective_mass_(solid-state_ph...
The particles still have exactly the same (positive) mass, they're just moving the wrong way due to wave interference.
If you want to be super misleading... why not call it a "tractor beam"? They're applying a push force but the particle is moving towards the push.
As others have noted, the abstract for the paper correctly characterizes the phenomena as "negative effective mass". That word "effective" makes all the difference.