Current Orientation

When you hold the Alt key, a legend appears with the text ‘Auto-Align’. Below, the current plane orientation appears, colored in pink/magenta, which you can change by scrolling your mouse wheel up/down when holding Alt.

Use the cursor rotation by selecting the LOCAL orientation.

The plane orientations for Auto-Align only apply to the origin of the world and cursor points, as objects on the other hand, can only use the global and local bounding boxes.