Rotating an object with a mirror modifier without affecting mirroring

In this tutorial:

at around 00:24, the mirrored plane is rotated and moved; however, the mirror modifier is not changed.

I tried something similar and can’t seem to rotate on an axis different from X without breaking the image (splitting the clipped planes):

How can you move objects around along with their modifiers (in this case mirror) without changing the effect of the modifier?

When you are in [Edit Mode] you are in the local space of the object. When you are in [Object Mode] you are in the global space of the object.

The mirror modifier is applied only on the local space. So it means that you can rotate the object in any way you want without affecting the mirror modifier in any way.