The press release at the top is very thin. There is a better summary and discussion at <https://bigthink.com/starts-with-a-bang/hawking-radiation-bl...>.

> Is it not equally likely that an anti particle falls into the black hole than a normal particle?

A photon is its own antiparticle. If a pair of photons is produced via a mechanism similar to the one in the paper from the press-release at the top then each can develop a very different trajectory from the other.

Conversely, an electron and a positron are each other's anti-particle. They have the same invariant mass. If they are formed as a pair, they can quickly annihilate (being electrically attracted to one another), or may in some cases separate (e.g. because of immersion in an electric field, as discussed in the paper and the summary of it by Ethan Siegel at the bigthink link above). A question then arises: if the Schwinger effect means a strong electric field can separate a positron-electron pair that pops into existence (taking energy from the electric field), can a strong gravitational field also separate them (taking energy from the gravitational field)? That's essentially what the paper explores, but using a simple electrically uncharged, massive, minimally-interacting scalar particle field for ease of calculation.

The model particle does not self-attract nor self-repel and does not require assessment of collinear momentum, particle decays, bound states, (inverse) Compton scattering, and so forth. The particles and antiparticles are indistinguishable; they just happen to pop up in correlated pairs. The trajectory of each half of the pair is freer to evolve in a gravitational field than for Standard Model physics (which has much stronger interactions than gravitation), but the simplified model plausibly translates to qualitatively similar results for real particles as we know them.

So, because there's no difference between the particle and the anti-particle (crucially the masses are identical) it doesn't matter which one goes which way. The argument in the paper for black holes (and other compact masses) is that some fraction of particles will fall inwards and some will escape to infinity, and the fraction is mostly determined by distance from the large central mass.

There is evaporation because the pairs pop up outside the black hole because its dynamical spacetime creates the equivalent of an acceleration (accelerations generally produce differences in particle-counts; the no-particle vacuum of an observer can be full of particles for an accelerated observer). Causing a particle-pair to appear outside it has reduces total mass of the black hole ("gravitational backreaction"). Hawking (and this paper) feed a fraction of the particles back into a black hole to make the spacetime less dynamic (in particular keeping the black hole mass constant), for ease of calculation.

The paper however goes further and generalizes the mechanism to any gravitating mass, not just black holes. A less-compact mass with no horizon (e.g. a neutron star) also causes particle pairs to pop up around it, and some fraction of those particles will fall onto the surface of the object as a reasonable proxy for a more technical treatment of gravitational backreaction. Many particles may hover around in the area like a very thin and very cold atmosphere. Others may escape to infinity.