A-coils collect moisture constantly as they are used..
The drain pan is there to catch the water and direct it to the condensation drain.
Wet A-coils and tubing can sometimes just be an indicator of the relative humidity.
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Think of those "radiators" you have called them as a place to collect water...like a dehumidifier. They remove the moisture in the air to lower the humidity in the rooms.
This is why you get hot when the temp is 85 degrees and the humidity is 90%....you sweat. Well to make this simple...the Radiator drips the water into the pan and drains to a hose.
If you have a lot of water in the pan you need to check the drain...or it will overflow.
This is all how A/C works ..sounds like its doing the job.