Brushless has no mixer because in the diagram they're using a GY240 on the gyro, negating the need for any mix at all. The brushed setup uses cheaper components and thus a cheaper rate gyro, which requires either a mixer (or) a transmitter with revo mix points. The diagram (and article) was based on a cheap route and expensive route comparison, which is why the images differ in the setup they show.

If you were using a rate gyro instead of HH, and you're not using a mixer, simply use the brushless wiring diagram and replace brushless motor with brushed and you're good to go.

As for the problem you're having, it sounds odd. If you punch or chop the throttle, is the tail swinging? Is there ANY stability on the tail before you give rudder command? It could be possible that you just reverse wired your tail motor or installed the prop wrong. It's also possible your revo mix is setup incorectly, and it's applying reverse input at revo point 3.