I’ve found that a simple rule of thumb for remembering axis directions in the Transformations panel is to imagine your left hand on the upper-left corner of the art.
For Z axis rotation, pull down.
For X axis rotation, pull the top edge toward you.
For Y axis rotation, pull the left edge toward you.
For X axis moves, pull left-to-right.
For Y axis moves, pull top-to-bottom.
Z axis moves is the one exception: push the art away from you.
To help visualize these axes, think about a basic 2D graph where X is horizontal and Y is vertical. In Illustrator, horizontal measurements increase left-right and vertical increases downward.
When this is projected to the left plane of the document’s axonometric projection, X and Y are consistent.
If we were to add a right face, horizontal measurements that increase left-to-right would coincide with the projection’s Z axis, so it makes sense to increase the object’s Z as pushing backward also. That, however, is the extent of a Transformation object’s correlation to the Projection panel’s axes. This is very important to remember: as an art object is rotated, its axes travel with it.
If you then move the object along an axis, it moves along the adjusted axis. It’s not limited to the projection’s three axes. This way, you can use any combination of rotations and movements to mathematically position the art in any orientation relative to the original flat view, then view it from any of eight preset orientations.