How does a mixed refrigerant provide cooling in a cold box?

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Our station is equipped with a pre-cooling cycle. Pre-cooling is separate. Propane evaporates in the pre-cooling heat exchanger, releasing cold energy to cool the natural gas and the mixed refrigerant. Natural gas is cooled to -30 degrees, while the mixed refrigerant is at over -27 degrees. The cooled mixed refrigerant enters the separator, where the gas phase and liquid phase refrigerants are separated. The liquid phase goes into the intercooler; the liquid phase exiting the intercooler is at -128 degrees, which is the temperature before the throttle valve. The temperature after the throttle valve is -130 degrees. After throttling, it enters the separation tank where the gas phase and liquid phase are separated; thereafter, the gas phase and liquid phase are combined again and sent back to the intercooler. Our cryogenic tank is equipped with three heat exchangers: a pre-cooling heat exchanger, an intermediate cooling heat exchanger, and a deep cooling heat exchanger. The pre-cooling heat exchanger is located at the top of the tank, the intermediate cooling one is in the middle, and the deep cooling one is at the bottom. Deep cryogenic vapor liquefaction, like the medium-temperature cooling process, will not be discussed here. I don’t understand now: before throttling in the intercooler and cryogenic systems, one temperature is -128 degrees and the other is -155 degrees. Where does this temperature come from? Some say it cools down as it goes lower. I think it is achieved by the evaporation of the refluxing refrigerant, which releases cold energy. It is obtained through heat exchange between the returning refrigerant, natural gas, and the downward-flowing mixed refrigerant. Is that correct? Who can explain it to me? There’s one more thing I don’t understand: after being throttled, the refrigerant enters the separator, where the vapor phase and liquid phase are separated, and then they mix together again and flow back. Isn’t this redundant? Since they have been separated, why do they mix together right after being separated? Who can explain this to me?