The black star promos that are legal are those with number DP01 or higher (yeah, they reset the numbering system AND the tournament legality), as well as POP 6 and up, in addition to DP-on.
The tin promos that are out now are all DP__, so yes, they're legal. Unless they are World Championship cards, in which case they wouldn't be. Unless it's known beforehand that you have them, you run your deck in sleeves, and the league leader allows it.