Yes I am referring to the control system in the dash.
Have you verified that the AC compressor clutch is in fact engaged all the time, or is cycling on and off all the time?
I'm not familiar with that control unit. Does it allow you to choose multiple outputs at once? For example windshield and lower footwell at the same time?
If the answer is yes, the system can only deliver AC air or non-ac air. Meaning I would expect selection of the windshield would override any other setting that would normally not be AC.
However, if you select only floor and dash and have not selected AC with the button, and the light is not on for AC, there should not be AC air coming out on the floor. Newer cars sometimes think they know better and will automatically engage or disengage AC, but I don't think they were doing that back then. Does this vehicle have an auto climate control or separate driver and passenger settings? Make sure they are both set to the same temperature when testing what's going on.
What year is this vehicle? I can point you to the circuit diagrams for the AC system. Is the AC button depressed and held in but not lit, or is the button out meaning disengaged but AC air comes out on the floor when it shouldn't? These are all troubleshooting steps and we can explore the possibilities on the circuit diagram. Usually it takes a lot of things to be in specific States for the lights like AC, defroster for the rear, etc to light up. They are usually one of the last things in the circuits so that if they are not on when they should be or they are on when they should not be, that is a big hint when analyzing the circuit diagram in comparison with what you see