What happens in the upper air when the altitude of the tropopause changes?
Short answer: I think the difference in the 2 soundings can be mostly explained by moving from one air mass (low pressure, relatively humid) to another (high pressure,  relatively dry) which also increases the tropopause height.

One thing you have to realize is that radiosoundings never provide a perfect vertical profile moving straight into the atmosphere with respect to the location you start your radiosounding but rather move with the wind. One thing that is obvious from your radiosoundings is that there is a strong backing of the wind, visible in the layer from the surface up to 500 hPa but most prominent in the layer from the surface up to +/- 700 hPa. Also, the wind speed seems to decrease slightly. These conditions imply that your location of the radiosounding near the height of the tropopause (may) have shifted significantly.

In combination with the temporal difference of 12 hours this may explain the discrepancy. From the first sounding to the second we also see advection of relatively warm, dry air in the 800-400 hPa layer. We find that temperatures go up, and the differnce between temperature and dry bulb temperature seems to increase. We also find that the surface pressure goes up, indicating a regime with higher pressure.

Still, we can not be certain that these conditions specifically apply for your radiosounding location. We can conclude that the above findings are speficially true for the pathway of the radiosonde.