To approximate with Newtonian laws:

F=ma

Meaning that positive and negative masses will accelerate in opposite directions in response to the same applied force. The effect is different, but it's a bit like how when you are in a car and hit the gas pedal, and your kid is in the back seat holding a helium balloon, the kid feels pushed backward into the seat but the balloon flies forward toward the windshield.

F = GMm/r^2

Meaning that gravitational forces between opposite signed masses is the opposite direction from the force between masses of the same sign.

Thus, the gravity force repels the normal mass away, but this repulsive force actually drags the negative mass along with it, because the negative mass accelerates the wrong way when "repelled".

We have an intuitive ~~example~~ approximation of this in real-life: balloons in a car[1].

[1]: https://www.youtube.com/watch?v=uAJlg8MDAlU

I'm intrigued. Isn't the reason a balloon moves forward more of buoyancy? If you do the same experiment with the window open, doesn't it do as expected by most people?

I didn't read that positive matter is attracting negative matter. What I gathered is that the presence of a cloud of negative matter in the right place would be held in place by mutual repulsion of the outer arms of the galaxy and the inner galaxy. And that the neg matter supplies enough repulsion to the diffuse outer galaxy that it can spin a bit slower than it would have to otherwise.