When on 30 amps, the Precision Circuits device should detect that there's no voltage differential between incoming L1 and L2, so it assumes that to be 30 amps and should start shedding loads when demand is more than 30 amps.
If you actually have 20 amps, or a malfunction giving you between 20 and 30 amps, the device has to be told that you have less than 30 amps so it can adjust accordingly.
I'm not sure what would happen in a low-voltage situation. If voltage from the pedestal drops 10% below nominal to 107V for example, amps will go up 10%. The Precision Circuits device may not be programmed to adjust for that situation. It might be thinking you have 30 amps when you actually are pulling 33 amps because of low voltage.
But that doesn't explain why it's not shedding loads - if that's the case. My understanding is that when the Air Conditioning load is shed, the compressor power is turned off but the fan is left running.
The numbers in the display may not be what you think. The manual describes them in a way that is not what you might guess.
Why don't you change the main panel setting to 20 amps and see whether it manages to a 20 amp supply. And if you have a voltmeter, see what the incoming voltage is reading.