Watering from underneath means putting the pots in water for 10 or 15 minutes. Don't let them sit for any longer or they will get too wet. Also, only water if they are dry or on mild days. They look quite happy!

Do as Volunteer says, what is more concerning is you have basically created a wooden box with a clear lid... A cold frame generally has no bottom and clear sides and top. I am concerned that your seedings will not get enough light from the sides and will therefore become drawn as they grow desperately towards the light.

Cold frames are usually made to slope from back to front, not the same height all round, usual height is 8-10" at the front, and15-18"at the back. they usually sit straight onto soil or some sort of aggregate, so the water drains away, if you can,t do this, I would suggest that you drill quite a few holes in the bottom to allow water to escape onto the slabs. It appears to be facing south,{assuming you took the picture mid afternoon} if so the position is ideal, as it will get the sun most of the day.
Hope this helps, Derekm.

Good points Derekm