Tell me how this works

I know when you keep your co2 bottle in the fridge the psi gauge reads low, but it still has the correct amount in there. my question is, if the gauge says its low due to the temp, how does the regulator let in the right amount of psi?

A full bottle of CO2 is mostly liquid.
A room temperature it will have vapor pressure of about 800 psi.
In the fridge, the vapor pressure is about 600 psi.
The regulator has atmospheric pressure, bottle pressure, and keg pressure.
It will allow CO2 to flow based on the difference between atmospheric pressure and keg pressure.
If you move the regulator from sea level to a mountain top, the pressure supplied to the keg will change.
But it isn't affected by temperature.

The reulator just regulates based on downstream pressure. It could care less what the upstream pressure is (within it's range). As long as the pressure is greater then the keg, the regulator will give you a constant pressure to the keg.