Your main job as healer is to heal the tank and the rest of the party. Try to keep everyone alive, make appropriate, timely heals while managing your MP to not overburden your party.

The healer DPS meta is just an optimization of play. Good healers are able to realize after awhile that they do not have to constantly heal the party in certain parts of an encounter. Rather than just stay idle or overheal, they discover they can supplement damage to help the run go faster. The better DPS oriented healers are able to damage-deal safely without wiping the party because of failed mechanics or missed heals.

If you want to get better at DPS while playing a healing job, you just have to practice. If you are unsure of how good the tank is with defensive cooldowns or if the party likes getting hit by things, you can cut back the damage-dealing and just focus on healing. Practice, practice, practice.