When and why are certain Chinese Emperors referred to as "The _______ Emperor" starting in the Ming Dynasty?

It seems to have started with the Ming Dynasty where our histories start to refer to Chinese Emperors as said in the title. What is the significance of this?

Every Emperor from the Ming dynasty has this naming template, but the first three sovereigns from the Qing Dynasty do not follow the same pattern as every other Emperor in the Qing Dynasty. Why is that?