Only time I ever had escapees was from a bucket (in transition from a worm-farm I had to leave behind), with only wet paper as a 'lid'. They started escaping after about 5 weeks.
In my case it was either: too wet or overpopulation. This was an inside situation too, but I have never had worms escape from Can-of-Worms kept outside. Regarding the tap - you can put a bucket under it and leave the tap on, if you wish.