I put my non-stop flowering tubers in blueberry containers and buried in sawdust for the winter and discovered that mice found them and ate some. I have stored these for years in my basement (Zone 5) and never had a problem. I always have mice that I trap over the winter. Just a warning.
Begonia Tubers and mice
You need a dog like my Westie, Tiffany. Or perhaps a cat. Sorry about your tubers. I scatter a few moth balls outside in the utility closet and near corners of the building where mice and chipmunks seem to want to hide. I wouldn't use them inside, though.