Regarding thermostats, like many others I use "auto" so that the heat & AC do what they are supposed to...all on their own. It's super convenient. Thermostats with "auto" modes, including my previous Honeywell models, and my 2 current Insteon thermostats, have TWO set points, one above which the AC turns on, and the other below which the heat turns on. (For "auto" to make sense, the "cool" set point needs to be a few degrees higher than the "heat" set point.)
On the Insteon thermostats, when you press the up or down arrows on the front of the thermostats, BOTH set points simply go up or down by one degree. You can do this from the ISY as well. In fact I have Alexa-voice-triggered IFTTT recipes tell the ISY do to the same thing. For example, "Alexa trigger warmer" tells the ISY to raise BOTH set points by 1 degree. Note that this might cause the AC to turn off...or it might cause the heat to turn on...which is EXACTLY what you want if you are using the "auto" mode.
Benoit, why not have the Echo "increase the temperature" function simply do the same thing. Completely IGNORE the ambient temperature if the thermostat is ON in any mode. If the thermostat is in heat mode or cool mode, simply change the set point by one degree. If the thermostat is in auto mode, simply change BOTH set points by one degree.
-Barry