Many (not all) chassidim keep them tucked in because the tallis katan is bechinas ohr pnimi on the inside and the talis gadol is bechinas ohr makif on the outside.
I have a good friend a tremendous talmid chacham and einikel of the Chofetz Chaim who says that he has a messora that the chafetz chaim did not wear the tzitzis of the tallis kattan out.
When he was asked how he wrote what he did about wearing them out, he replied that he meant that if one is wearing the talis katan outside then one should not hide the tzitzis by tucking them in, but he did not mean pulling them out if the the talis katan is under the shirt.