Really, Davkis.
Each role has more responsibility than others in different battles.
Titan? Role with the LEAST responsibilities is tank. Not saying he has none, but damn if tanking Titan isn't 20x easier than DPSing him, all the annoying mechanics avoid you.
Garuda? Least responsibilities fall to healer, if everyone is doing their job right the healer should worry only about the tank.
Ifrit? HM is... Really only responsibility is the stunner but then again at EX the LEAST is the tank's, you do little more than keep Ifrit facing you, highest goes to healer with not just healing but also not TPKOing the party.

Turn 1? That's a tough choice for the least, but i'd drop it on the DPS who isn't dragging slimes.
Turn 2? Very, very tough call really since the main mechanic is partywide but i'd call it on the melee DPS this time since he'll prefferable be out of rot rotation due to positioning.
Turn 3? Everyone? Like, really.
Turn 4? Tough call as well, anyone fails it's going to hurt, i'm going to call it on tank as you get a moment where you can stop and breath and take a moment on auto for a while while the DPS work on killing everything fast enough. But only a tiny margin there.
Turn 5? I'm not sure I can say anyone has any less responsibility at anything here