Alternator rotate in reversed direction: does the induce emf violate the Lenz's law?

There is a question in my textbook:

Below show the structure of a bicycle alternator:

And the output terminal is connected to CRO to show the induced emf. When the magnet is set to rotated in one direction, the CRO shows the following trace:

The question asks me to draw the new trace if the magnet is set to rotate in opposite direction with the same speed.
And the answer for that question is:

And I was thinking: why the direction of induced emf is reversed when the direction of rotation of the magnet is reversed?

My work:

The magnetic field (B-field) of magnet point from N- to S-pole. And the soft iron is used to guide the B-field line through the coil. Therefore, when the poles of magnet approach or leave the ends of the soft iron, the upward/downward B-field through coil will increase or decrease respectively. According to Lenz’s law, the induced current should flow in a direction so as to oppose the change causing it; with Right hand grip rule, we can find the direction of current flow between X and Y if the circuit is completed. As the direction of induced emf should be the same as the induced current.

Therefore, I determine the direction of indeced emf (same direction as induced current) by the above method for both direction of rotation of magnet:

And my conclusion should be no matter which direction the magnet is rotated, their direction of induced emf should be the same at any time, the new trace should be exactly the same as the original trace in CRO.

But this is different from the answer from my textbook. So I search around the Web, i found a similar question: When the alternator is made to rotate in opposite direction will it effect the electricity generated?

What is different is the phase of the voltage relative to the position of the alternator shaft at any instant. For opposite rotations, the phase shift will be 180 degrees.

But i still don’t understand about that, how can it be different from the result of Lenz’s law, does it violate the Lenz’s law?

Or did i did something wrong when predict the direction of the induced emf?

If there’s actually a phase shift, could anyone explain what’s the origin of it?