If you're referring to column mounted prndl stalks, they don't turn with the wheel. Examples: Mercedes, older Model S, and lots of pickup trucks.
If you're referring to paddle shifters, ironically Ferrari (of wheel-mounted indicator buttons fame) mounts them on the column instead (again, not turning with the wheel). IMHO both are fine for street and track usage because manual shifting is most likely triggered when the car is (almost) straight. However this assumption does not apply to turning indicator controls, which by definition are used when you are, uh, turning or about to turn!
If you're referring to paddle shifters, ironically Ferrari (of wheel-mounted indicator buttons fame) mounts them on the column instead (again, not turning with the wheel). IMHO both are fine for street and track usage because manual shifting is most likely triggered when the car is (almost) straight. However this assumption does not apply to turning indicator controls, which by definition are used when you are, uh, turning or about to turn!