Maybe it was modeled as a curvature of space? So positive masses curve space so that everything moves toward them - including light, massless particles, and negative mass. And negative mass repels everything, including other negative mass, by shaping space differently.

[Edit: jbay808 has a better explanation below, and negative mass attracts negative mass.]

That behavior is described here https://en.wikipedia.org/wiki/Negative_mass#Runaway_motion but it's not what I was expecting either.