The problem you have is given because there is no communication between the button that acts the AA compressor and the engine injection switchboard.
This is easily noticed that when you put the air conditioning the engine accelerates a bit. In gasoline carburation engines, there is a lung driven by a solenoid valve and the engine vacuum that pulls the accelerator cable so that the regime rises and does not heat.
The injection switchboard provides an "extra" amount of fuel when the air conditioning is on to prevent the engine from being easily covered in deceleration cuts, the gasoline supply is reestabbed from 1500 rpm instead of the normal 1000 rpm.
The failure must be in the button itself, in the wiring or in some relay, if you can take it to an electrician who looks at you.
I hope I have helped you.