Is this a home made setup, or a commercially available worm bin?

The idea of worm "tea" is just fluff, because compost "tea" is fashionable at the moment and worm promoters want to try and make leachate from a worm bin sound like a fabulous asset instead of just waste product. Ideally, leachate coming out of a worm bin system should be kept to a minimum. It's hard to avoid sometimes, but it also shouldn't be encouraged. Your bin should have a way to drain off the excess leachate - it should never be allowed to collect in a pond in the bottom, because it will get stagnant and smelly. Worms don't drown that easily, and they can usually climb out of a little water if they happen to fall in, but stagnant leachate can grow noxious anerobic bacteria and give off vapors which are harmful to the worms and unpleasant to the worm-herder.

If the worms can go through the holes in your bin one way, they can always go back the other way, so I don't think they're getting "stuck". What usually happens on the inside of a plastic bin is that any area where some moisture collects is bound to have worms crawling along it. They don't like to wiggle into dry places or into light, but they just love to explore anywhere there's a little condensation. If you see them clinging to the insides of the bin they're not "stuck," they're just on walkabout. It won't hurt them to wander through empty parts of the bin as long as there's moisture there, but there's also no reason to have an empty tray in there - you can just take that one out until you have filled the first tray.