Your example is correct for a solid disk. However the rotor is not solid so a different set of physical
principles apply. Gyroscopic precession does not really apply, resonance does.
A rotor blade acts like it is spring loaded, centrifugal force tends to pull it flat, other forces
tend to push it away from flat. Vibration analysis shows that when you push on something
with a spring it tends to keep going after you keep pushing. The distance that it keeps going is
the maximum displacement. The maximum displacement occurs after the maximum force. If
you hold a slinky in your hand and let it dangle, then push down and stop, the bottom of the slinky
keeps going after you stop. This illustrates how displacement is behind force. A kids paddle ball toy with
a paddle, rubber band and ball does the same thing. You hit the ball but the ball keeps pulling out (displaces)
way after the ball has left the paddle (the force has stopped).

In your rotor, if you tilt the shaft to the right, the blade that is at the rear gets tilted right, and therefore
negative. This creates a push down on the blade in the back. It displaces (flaps) down, but after the force
is gone. It turns out that the maximum displacement is 90 degrees later on the right side. The blade in the
front gets positive pitch, an up push and 90 degrees later flaps up on the left side. This is how right tilt creates
right rotor disk roll.
Your solid disk when tilted right will tip down in the front. A rotor when tilted right will tilt right.
mick