The expression means you're going to be the best or achieve the highest possible result in any given situation. The phrase originated from a player named CrazyPsychopath (Twitch name: Praetor Pyro) in the game Command and Conquer Rivals. The highest league in the game is Tiberium league, thus, to get the "dibs on the tibs" is to say that you're going to either be in Tiberium league first or you're going to get double Tiberium (with both factions) soon, as you're striving to get there.
by BadMoscowMofo August 10, 2019