Yep, things can walk out of the jaws if the steady's not on Centre - easy way to get 99% there is to indicate in at the jaws, then a couple of inches out. Now slide the steady up to where you're indicating and adjust the fingers WHILE WATCHING THE DTI, finally loosen ONE finger and slide into place, then readjust the finger you loosened - I've done it this way for years (when possible), haven't has a part walk yet!
EDIT: the part can't rotate in a 'cone' as both ends are constrained, Chuck at one end, steady at t'other, what it does is rotate at an angle to the spindle axis, so it frets against the jaws and works its way out.