Megan, looks like a really old manual, maybe from when Igor Sikorsky was an instructor on your course.
Note that it says "precession is not a dominant force", and adds that a rotor exhibits "some" of a gyro's characteristics.
The second section about nose up or down when rolling into a turn is something that I have never observed in 45 years and 15,000 hours of rotary flying. Either I have been totally blind to such things happening around me, or they are confused about what is happening. Rolling into a right turn means the swash plate is causing the blade pitch to be at a minimum over the tail to reach the lowest point at the right side. The whole disc tilts right, the fuselage follows. The "precession" has already happened over the tail and over the nose to make the disc tilt right, it is not a force applied at the right side to tilt the disc and having a "precession" effect 90 degrees later over the nose.
Or is my brain fried after all these years of being bounced up and down at 2:1 and 4:1?