cold DRY air is descending thru/in the eye.
I do not think so. I think that the air in the eye is HOT and dry.
The answer would start with this:
What goes up must come down.
In an ordinary cyclone, warm moist air rises - drops the rain, reaches the heights as cold dry air - and it has to go down. When it goes down, it ends up as dry air which is warmer than the original warm moist air - because it has gained the heat from the condensation.
In the ordinary cyclone, there is calm wind - because of symmetry - but heavy rain in the dead middle. Around the middle of the cyclone, the air spirals up, causing a windstorm and rain. At the centre, the air goes straight up, causing calm wind and heavy rain.
The air which reaches the upper levels above the cyclone flows out at upper levels, and then descends outside the cyclone, causing warm and dry weather.
This description also applies to weak tropical cyclones.
However, in strong tropical cyclones, so much air builds up at the upper levels above the typhoon that while most of it still flows out and descends in neighbouring areas, some forces its way straight down the middle of the cyclone, suppressing the rain and clouds there. So the air goes up all around the eyewall and comes down both outside the typhoon and inside the eye!