After a closer look at the results, it looks like everything was physically reasonable. There was some very quick action that was happening during the first 2e-5 sec and 0.15 sec that created the initial spike in the T_I of the cylinder. In fact, it's more than a simple spike.
0 ~ 2.5e-5 sec: vapor rush into the cylinder (mdot_A), pressure quickly rises (p_I), T_I quick rises because the incoming fluid is doing work to the volume. At this time, there is a huge amount of force applied by the cylinder on the mass because the initial force from the spring is zero. The mass will accelerate quickly.
0 ~ 0.05sec: the mass is accelerated quickly to 30m/s, expanding the cylinder volume. The pressure and temperature drops quickly because mdot_A can't keep up. The net force on the mass crosses zero ~0.035sec as the spring is compressed enough.
0.05 ~ 0.15sec: mass still moving away but slowing down. mdot_A catches up, doing work to the low pressure volume, increasing both the pressure and temperature. Around this time, the spring force starts to match the cylinder force and the volume starts to stablize.
After that, things start to approach steady-state.
During the process, the temperature of the chamber drops a little bit, while also fluctuates according to the sign/direction of mdot_A. That's also where all the energy comes from.
Hope this makes sense.