I mean, it is random. It's kind of like slots. When it gives you your three options, each character is given a random roll between their three quickenings and Mist Charge.
So let's say you're Balthier, and you used his lvl 1 Quickening. When the roll comes up you might get his lvl 1, lvl 2, lvl 3, or Mist Charge. If it's lvl 1 or lvl 2, you can select it, because since you originally used his level 1, you still have 2 bars left. If lvl 3 comes up, it'll be greyed out cause you no longer have enough bars to cast it (because you already used one to initiate the Quickening). So you have to choose another character's option or reroll with the R2 button. If it's Mist Charge, you'll get all his bars back and it will reroll so you can select something new. And this time you'll be guaranteed to select Balthier again, because you've given him all his bars back, so no matter if it's 1, 2, or 3, you'll be able to cast it
So if you want long chains, you'd want to select low level quickenings, because that leaves you with more mist bars available to you, so your odds are better of a roll coming up with something you're still got the bars left to cast. If you consistently use lvl 3s, you become reliant on Mist Charge showing up on the slot reel to refill that characters bars and give you the ability to continue the quickening chain.
