A lot of people have compost outdoors and worm bins indoors. I do. I put the leaves and grass clippings in a place outdoors. The peelings and leftovers and such I put in a worm bin in the basement. My favorite thing about it is that I can do it year-round. No tromping through the snow to get to an outside compost pit in the winter. Also, the worms seem to get things done faster.
However, if the kitchen garbage seems to be accumulating faster than the worms can keep up with at any particular time, I can always throw some of it in the outdoor compost bin. Conversely, I sometimes take some leaves from the outdoor bin and put them in the worms' indoor bin for bedding.
If your "wild" worms are hanging out in the leaves, then they are probably the epigeic type, and will do fine in your bin, no matter what specific type they are. It's worth a try, anyway.
Betts