How would it work in the southern temperate regions?
In the southern temperate regions, the moon spends most of its time to the north, so we would observe it facing north. Thus the moon rises to our right (the east) and sets to our left (the west). So the daily motion of the moon is from right to left (east to west), and the monthly motion is from left to right (west to east). The calendar would be drawn with the days increasing from left to right. The new moon which starts a lunar month would be drawn at the far left followed by the waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, waning crescent, and subsequent new moon in order from left to right.