[Teeps]

The a/c compressor on all Honda/Acura models cycle on/off when the evaporator temperature is just above freezing.
This is normal as it prevents the evaporator from icing.
It is not normal for the compressor to be "on" when the A/C button is off.
Note: the a/c compressor operates when front defrost is on. But the a/c "on" indicator does not illuminate.
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[Teeps]

Ok.
Does the condenser fan run also?
If not could be faulty compressor clutch relay

 

[Teeps]

That is not correct. The rear window defroster being on or off has nothing at all to do with the A/C compressor in any way at all. The A/C compressor cycles on and off due to it only builds a set amount of pressure and also only gets the evaporator so cold before it turns off again. the reason it is doing it without you having the A/C turned on is that if you have it turned to defrost setting or feet and defrost setting the A/C is used in all defrost settings on the HVAC setting not the rear window defrost being on. It is so it can remove moisture from the front windshield and the rest of the interior windows as well if it can as well depending on the amount of moisture in the air. That's part of why u always see water dripping out from under your car in summer is the removal of moisture and the cooling of the evaporator.
Sorry just needed to correct this one as I was a Honda tech for 2 years as well as I'm a licensed Tech for over 15 years now.

Don't be sorry.
And you are correct; I should have checked my facts before posting.
below from 2012 Civic ower's manual.