Both boiling and evaporation involve changing a liquid to a gaseous state. Both are driven by the liquid/vapor system not being in equilibrium as far as the actual vapor pressure vs. The vapor pressure associated with the saturated state.
Boiling means the conversion process is happening throughout the bulk of the liquid and bubbles are forming. Evaporation is the same process, but it is happening on the surface of the fluid.
The refrigerant compressor pumps vapor. Let's assume it operates on a constant volume basis. The pumping rate is proportional to vapor density at the pump inlet. Cooling the vapor at constant pressure increases density and flow rate. Increasing the pressure at constant temperature increases density and flow rate.
At the expansion valve, fluid is being pulled through because the compressor is removing vapor from the exit side of the evaporator coil. The fluid at the expansion valve inlet is liquid. By design, you don't want vapor there. The exit of the expansion valve is mixed phase. There is a big pressure drop across the valve. As soon as the fluid enters the low pressure side, some of it flashes to vapor. The refrigerant will be in saturated equilibrium at the low-side pressure. Most of it is still liquid, but it is bubbly. The remaining liquid gets vaporized in the evaporator and cools the room.
A TXV valve like in the video has two inputs. There is a knob that adjusts the pressure drop at a given sense temperature (only to be adjusted by a qualified tech), and a temp bulb that senses the evaporator vapor temperature and changes the size of the passage in the valve. The result is a complicated balancing act.
If the valve closes a bit (because the bulb senses too low a temp in the vapor line), the pressure difference increases. After a bit, the low side of the valve (bubbly liquid line) will be cooler and lower pressure. And the flow rate will be less as well. The density of the vapor on the low side will be less. This is the key result. By design, closing the valve a little results in a lower vapor density at the compressor inlet, reducing flow rate, and ensuring that only vapor is getting sent to the compressor. The lower flow rate means the vapor line temp rises, providing the system's negative feedback. You can't show this by just looking at the valve - you have to look at how the entire system responds to the valve, and it is designed so that it responds this way when working properly and properly charged. It may not work this way if there are problems in the system. Lots of these valves get replaced when they aren't bad, but the tech didn't find the real problem.
The TXV valve effects a change to the refrigerant flow rate. It senses the vapor line temperature, and changes the flow rate to keep the vapor line temperature above the saturation temperature. Most are pressure compensating so that in effect, they do a decent job of maintaining a fixed superheat in the low side vapor line.
Compare with AXV, automatic expansion valve - https://neilorme.com/AEV.shtml