I've heard that sometimes the catching prey but not killing it comes from the kitten not being left with the mother long enough to learn to kill. But you said she kills sometimes. Maybe she does it for fun. I mean, hunting is exciting for people and that's why they still do it even when they don't have to. I'm sure the same goes for your cat. I've also heard that cats consider humans to be inferior hunters (unlike themselves!) and when they love you and care about you they will bring prey to you so you are taken care of and fed. Pearl did this when I first got her, she was always an inside cat, but she killed roaches and lizards that were always getting in. No matter how clean your house is or how much you spray, in Florida there are always some kind of bugs getting in. She left a dead roach out for me one morning, so I petted her and praised her lavishly so she would keep killing them. But since you aren't real pleased with Tiger's 'gifts' just dispose of them quietly, don't yell at her or make like you are mad about it. She won't understand.
Since it's so distressing that she brings live animals into your house, I'm going to cast my voice in with the rest that say keep her inside. If she's really going to go bonkers without getting SOME outside time, consider building her an outdoor run. She won't have an opportunity to catch critters in there.