I have been facing this problem and have been to the mechanics on quite a few occasions without any luck. For some reason whenever I switch the AC of my Corolla 10th Generation, the mat on the right hand side (drivers side) gets completely soaked with water. If I take the mat out I can see the floor flooded with water and have to take it out manually.
The drain is working fine apparently, as it is located on the left hand side and the water is leaking on the right hand side. Furthermore, when I took it to the AC shop, the guy told me that their is a possibility that packing of the box in which the inner coil is located might have gone bad, which is causing for the water to leak from there. However, the airflow from the aircon is perfect.