OK, so let's talk about Timetwister. Timetwister is one of the Power 9, and while maybe not in the top 10 cards ever printed in raw power, it was up there. You might notice a red card that reads very similar called Wheel of Fortune. I'm going to talk about Wheel, because it's used slightly differently than Timetwister, and I'm going to explain why the same concepts help Tibalt.
First, what do they do? Well, 2R: Draw 7 is clearly very good. But, it has a drawback. First, you have to discard your hand before you get the goods, and second, your opponent does the same thing. Why is discarding your hands and drawing new ones advantageous for one player? Heck, you're spending mana to do it! Well, that's true, but hopefully you realized you had Wheel in your deck while you were building it, and all of the cards in the deck cost very little mana. That way, you can dump your hand, or most of it, by turn 3 or 4, and ideally faster than your opponent. If your opening hand was 3 Mountains, a Goblin Guide, a pair of Lightning Bolts, and a Wheel of Fortune, you can see where it's quite a powerhouse.
Well, duh, draw-7s are good. Why is Tibalt like a draw-7? Simple; he belongs in a deck that knows what his abilities do. As another poster suggested, one way to do that is to make graveyard interactions. But, like Wheel, another way is to just make your deck full of cheap cards. A good Red Deck Wins style deck only wants to draw 3-4 lands; and more than that is useless. In addition, after a certain point, creatures are useless, you only want to draw burn spells. Tibalt looks at your turn 4 hand of Mountain, Mountain, irrelevant creature, and says "Here, have a 75% chance at a new card." It isn't perfect, but doing it every turn for 2 mana is really good. But wait, there's more! As you continually improve your hand, you're building up to an ability that could dish out a lot of damage, either his -4 OR his -6.
People will hate on discarding at random, but if your deck has cards that are just dead after a certain point, spinning the wheel is helpful. And if there are a few turns he sits there NOT drawing cards, because your hand is good, then your hand is good and you didn't need the help. It doesn't have to just be a RDW; your R/U counter/burn deck also wants limited lands, your hand is land, land, Think Twice, Mana Leak. Your opponent is playing around the Leak anyways, discarding the TT isn't a big deal, and you don't need lands. That's a few turns of spinning that wheel and profiting.