Luvmathur
Would you remember that when you mentioned "drift left - T alt increases and drift right - T alt decreases" was it applicable only to the NH or both hemispheres
Go back to basics and work it out for yourself.
At the Equator the surface of the Earth moves to the east at about 1000 knots. In still air the air moves at the same speed as the surface.
If we move north or south of the Equator the circumference of the Earth decreases so the speed at which the surface moves east also decreases. But if air is moved north or south it tends to retain its eastward speed. This means that the air is now moving east faster than the surface. The overall effect is that the air tends to turn to the east as it moves north or south of the Equator.
If we have a low pressure area in the north the air is drawn towards it. The eastward movement of the air causes it to rotate anticlockwise around the low pressure area.
If we have a low pressure area in the south the air is drawn towards it. The eastward movement of the air causes it to rotate clockwise around the low pressure area.
So the effect of drift in the southern hemisphere is the opposite of that in the northern hemisphere.