Joey uses Time Wizard against several other notable Duelists, including Mai Valentine and Seto Kaiba
So its quite clear that this one, despite having the classic card number of LOB-EN070 (which all of the Red-Eyes Black Dragon cards from The Legend of Blue-Eyes White Dragon sets have), is quite an easy card to tell apart from the others
Since this archetype hasn't been updated to reflect other aspects of the game, such as Synchro Summons, Xyz Summons, and Link Summons, there should be new Reactor cards to reflect them
However, Dark World effects dont activate after every instance of being discarded
It does not have to activate its effect during the End Phase to shuffle itself into the Extra Deck
An in-show example comes from the Crow-vs-Jaeger duel in 43/44: although Jaeger makes no secret of the fact that he's cheating by looking up information on Crow's deck during the duel, Crow gets a heads-up on what Jaeger thinks he will do because the holographic computer Jaeger is using has a screen that's also readable from the other side