I dont think that is how it works. propane is liquid, you will only get so much in there and they fill by weight. even if it was gas, as soon as it starts to fill it will instantly warm up caused by the fill pressure negating any chill effect.
Propane in a tank is technically "gas over liquid". When "full", a 20lb tank has 20lbs of propane, but there is volume of the tank that contains gas (i.e. the tank is not 100% full of liquid), this is why you can't use a tank on its side unless it is designed to be used this way with a pickup tube clocked to the 12:00 position, you'll dispense liquid instead of gaseous propane.
The propane coming from the bulk tank (your filler) is already liquid. It is not going to be compressed any further by any part of the fill operation. There is no "heating up" from the fill pressure. The pressure on the supply side is literally the vapor pressure of the propane at room temperature. (
Approximately 110psi @ 70F)
When you transfer liquid propane from the bulk tank to the portable tank, the liquid propane will absorb some of the ambient heat energy from the tank as it expands into the space. You cannot completely prevent some expansion, as the volume of the tank is fixed. If the tank was like a balloon, and expanded as more liquid was added, then you could keep the propane almost entirely liquid, but since the tank is rigid, there's a brief period where there's a small amount of liquid propane in a (relatively) large empty volume, so the gas will expand to fill the volume and in the process absorb heat.
Now, the faster you fill the tank, the more you can minimize this effect, because you're replacing the "empty" volume with more liquid, offering less reserve volume for gas expansion. Conversely, if you were to try to "slow fill" a tank (like say over the course of an hour), you would have a hard time getting 20 full pounds of propane into the tank because the gaseous propane would be occupying most of the volume and you would have to re-compress the gas to make room for the liquid - which you can't really do without a compressor, since you only have the working vapor pressure of propane on your side.
In all of this, in order for the liquid propane to expand to fill the volume of the tank, it needs to absorb heat energy from the surrounding environment (the tank). Pre-chilling the tank creates a temporary deficit of available energy, so that when you start adding the liquid propane, there is less available energy to "boil" the propane and more of it will stay in liquid form. This is a sort-lasting effect, but it can make the difference between getting a "full" 20 lbs into a tank or just getting 18, for example.
On a smaller scale - watch someone fill a CO2 paintball tank. Depending on the flow rate of your fill rig and the ambient temperature, it can be almost impossible to "fill" a tank by weight without pre-chilling because there is so little reserve volume within the tank.
