Difference between a right roll and a left roll
To avoid confusion, don't think in terms of what happens to the arm.
Rather, see Figure 7 and think in terms of what happens to the red axis.
A right roll in an airplane causes the right wing to tilt downward. (See Figure 3.)
A right roll around the blue axis causes the red axis to tilt downward.
For the coach's left arm, if the red axis tilts downward, then the arm proper will tilt upward as shown in Figure 11.