duppiman: Welcome to ATP!
I've used self watering containers in the past for Gesneriad type plants (African Violets etc.) If you water from the bottom reservoir and the soil is wet at the top, the roots may be totally saturated. Self watering pots allow the plant to take up water from the bottom as needed and it sounds like the soil in your pots may be holding way too much water. I'd remove the plants from their pots and inspect the roots to make sure they are not rotting; even though the reservoir is empty the soil around those roots can remain quite wet so the cause of leaf wilt can indeed be from too much moisture.
As Hetty stated, Colocasia plants prefer an atmosphere of high humidity and a tray with moist pebbles for the pot to sit on will help raise the humidity level around the plants.
As Evan said; an airy/well draining soil will help with proper drainage. I use a mixture of potting soil and lots of orchid bark mix for everything I grow. It makes for a chunky, aerated and well draining medium and I just adjust the watering as needed because some of my plants prefer more water than others.
Again,
to ATP!
Lin