in the southern hemisphere the CAT is encountered on the top southern side of the jet stream
CAT is generally encountered on the
lower, southern side of the jet stream.
The increasing TAT has me stumped. TAT is related to the OAT and your IAS.
But closely follows the OAT up and down. Don't know why it would be increasing whilst heading south?
Simply put, the jet forms where the warm air and the cold air meet, with the warm air to the north, and the cold air to the south (southern hemisphere). It is well depicted on the BoM SigWx Charts. You can see the different heights of the tropopause shown in boxes on the chart.