When using GH to set the temp in “auto” mode things are a little wacky. The way it should work (and does with echo) is the requested temp will be the midpoint of the heat/cool set points. So if I ask for 71 and the Ecobee has a 2 degree offset, it will properly set the heat to 70 and cool to 72…
What its actually doing is only changing one set point to the requested temp and the other will be 4 or 5 degrees higher or lower. If your asking for a cooler temp it will change the cooling set point and vice versa.
Example: I have the system in auto mode with a 2 degree offset and aiming for 71 (heating to 70 cooling to 72). I’m cold so I tell Google to change the thermostat to 73. Instead of adjusting the heat point to 72 and cool to 74 it will set heating to 73 exactly and cool to 78.