worms love melon - but as you have found out - seeds do grow
if it is really wet tray adding cardboard / paper to the mixture to soak up the excess, generally worms moving through the compost should create drainage channels so the water can pass through, unfortunatly if there are no worms then the compost compresses and gets wetter - then you end up with the situation where air cannot flow through either.
Give it a mix up with a trowel and turn the compost over and hopefully your worms will then go back down and eat the food.
Rain water will get into the trays but shouldnt flood them
Good Luck
Ronnie