I can't speak specifically for you model, but on most cars, the auto climate control uses the engine vacuum to operate. There is usually a 'one way' valve to hold the CC vacuum when the engine's vacuum drops.
On higher mileage cars, either the related hoses start to leak or the one way valve leaks. You open the throttle(in gear), vacuum drops, CC sees the lower vac and gets confused. Close throttle, vac up, works normal.
If you blip the throttle without load (not in gear)usually the CC will not be affected.
Hope this helps, Jim
'91 Miata Turbo 280hp
'90 Miata Turbo 230hp
'90 Audi 200 turbo