The actual axis direction of movement is a very controversial subject because it usually relates to the position the operator stands in relation to the machine and is usually defined (at least within Mach) as the direction the tool moves relative to the workpiece.
That Haas diagram is also confusing because it appears to show the direction of axis movement which would be incorrect - in fact it shows the direction of tool movement in relation to the workpiece.
This pic from my machine shows the actual direction of axis movement.