You have to make at least 1 attack on the fate or boss.

Also, healers in FFxiv are played a bit different.
For example, in a standard 8 player group of 2 tanks, 2 healer and 4 DPS, the healers contribute 15-20% of the overall DMG.
Let it be through buffs on other player or in case of a WHM by his own DMG.

The general rule for healer and caster is the ABC.
Always Be Casting.
So, if your group is at 80%+ HP and and no one is dead, then you should be casting your dmg spell.
And every healer has a dot spell. You should have the dot active one a boss for 100% of the time. You should refresh it when it has 5 sec left, so it never runs out.