Technically all of these are tier 1, as they all share the same set bonus. Tionese comes from hard mode flashpoint bosses that aren't the last boss, and can be purchased with commendations and crystals that drop off bosses and dailies. Columi comes from the last boss of a hard mode flashpoint, and normal operations, and can be purchased with commendations that drop off bosses and dailies. Rakata comes from hard mode and nightmare mode operations.
Has the community built out a comprehensive list that associates particular pieces of gear with particular bosses? Eg:
Tionese legs drop from boss x in FP A.
Columni bracers drop from boss y in FP B.
From what you wrote, for the different gear, a piece (let's say Columni head gear for the sake of the example) can either a) drop or b) be purchased with commendations/crystals.
Is this an either/or proposition? In other words, is a piece either a drop OR purchaseable? Or are all pieces available as drops AND purchaseable items? Is this true of every armor grade?