Just to clarify, I should have said "lift the lid off each day". No need to lift the punnets. You need to check for germination, as mentioned in the video, but also check for musty smells. If things seem to be going a bit fungal in there, leave the lid off for at least an hour a day, but the 23 or so covered hours will still help to keep your seeds moist.
The polystyrene box has no drainage holes. It can also double as a watering tray.