Oh cool, that makes a lot more sense. I was already on edge and couldn't really tell if it worked the time I tried it, so I switched to hard targeting.
That's actually a relic from how FFXI targeting worked (which is one of the few interface mechanics that carried over to FFXIV).
You have a target, and a sub-target. The sub-target selection goes away after using one action, so you can go into situations like healing the tank, but you need to patch up the DRG because they're a DRG, so you press down to sub-target them, Cure, and then because you no longer have a sub-target after using that action, you're back to targeting the tank.
It's also helpful in situations where you're DPSing enemies and need to toss a heal or Regen or something quickly on someone, without losing too much time - set the enemy as your target, sub-target whomever needs a heal, cast it, and continue with your DPS like a healer should.
Similarly, as you can probably guess, it's handy for tanks to cycle between secondary targets for different parts of an enmity combo, or for stunning/silencing/dotting a separate enemy from the one you're focusing down as a DPS.
This and properly setting up target filters and the Expanded and W Cross Hotbar are things that really, really should be in a tutorial in this game, but they aren't. They're imperative to playing well on a controller.