It's people like Jaelommiss that cause wipes.
I HATE it when people refuse to cast Esuna in groups.
There are some dungeons where there are DoTs that are very powerful, sometimes downright lethal. Anywhere from that sand dungeon I can't remember the name of for trying (the 2nd boss, the sandworm) to Mist Dragon, to a plethora of bosses that like Damage Down debuffs, or situational debuffs (the Tome in Gubal Library slowing someone is pretty much a death sentence if it isn't Esuna'd fast), or how about that scorpion in Sastasha Hard? Not Esuna'ing that is almost a guaranteed wipe. Either way, having a healer that refuses to cast Esuna sucks.
As for Cure.... Cure is a hard-casted heal that casts faster than most spells and sometimes it can just barely save a life, especially if it were to crit. When you are Sync'd, or your Tetra was already used, Bene's gone, and you're out of flowers... Cure is that quick cast that might get you out of a jam. That, and if you get synch'd, then what?
As for the OP... I know my advice is not popular, but...
At first, Cure is going to be your main heal. Cure II will eat your MP like crazy. This isn't Stormblood. You're not meant to spam Cure II as your main heal. You now get flowers at regular intervals and you get two new heals: Solace and Rapture. Single-Target and AoE respectively. Using 3 of these causes the big red flower to grow until it activates Misery which is a powerful AoE damage spell.
Solace and Rapture are **NOT** oGCD -- they are instant but will trigger GCD. Don't treat these like oGCDs.
You got Tetra and Bene like usual, Benison is still there and it's still good to use on a regular basis.
They nerfed Medica II's HoT, so don't go relying on that. Again, this ain't Stormblood.
Plenary Indulgence makes your next one or two Medica/Medica II/Rapture heal for pretty much double (or more) than it would have normally healed, hopefully everybody is within range when you pop it.
And don't forget about Assize which seems stronger than it used to be? Not sure on that.
Otherwise.... it's mostly the same.