Some of those tips are greatly exaggerated. First of all, us healers heal first, dps is secondary. A WHM can solo heal 8 man parties if needed, and are not secondary healers.
"Those who would walk the path of the white mage are healers without peer, possessed of the power to deliver comrades from the direst of afflictions—even the icy grip of death itself." - Jobguide
Cure II is used late game, as sometimes the tank will be hit like a truck, and other times like being hit with a rolling train-wreck. Sometimes one can use CureII+Tetragrammaton to bring the tank from 20-30% to 80-90% when Benediction is on cooldown. Healing/damage varies in the dungeons, and is something one learns to account for, and sometimes different strategies for healing that one are unfamiliar might occur, and require a bit of improvisation. Since WHM don't have proper shield magic before lvl. 66, HoTs and Asylum make healing less stressfull, especially combined with Largesse. After applying HoT you can put up an Aero I+II now and then - it's not required, but lower the time having to heal. The lilies sadly aren't really something that need a lot of thinking about, they are mostly just there, and nice to look at. Cure 1 is mostly used on the ranged dps, or you can use Cure III if there are melee near the tank that got hit with an aoe. Medica (+/- Plenary Indulgence) is more effective and faster than Medica 2, but when to use either still depend on the content.

Holy spam can be done, but it takes a lot of mp without Thin Air (lvl. 62), and the tank will die if done indiscriminately. Swiftcast+Holy(+Assize) combo can give you a bit of breathing room to get a situation under control, and pick off the small mobs with little health left, allowing tank/dps to focus on the larger ones.

Just remember to be a healer foremost, and if you're comfortable/bored then apply damage