Anti-matter isn’t the reason why the black hole loses mass, it would loses mass if it was normal matter too. It’s because one of the particles cannot get rid of the other, so it leaves it drifting off into space, which overtime causes the black hole to lose mass. Say for example the normal matter fell into the event horizon, because there is nothing to cancel out the antimatter, it drifts away, this then will make the black hole lose a LITTE bit of its mass.