There’s a few things to consider when deciding how to heal the damage:
1. How many players are taking damage? Remember that Ancient Teachings is split evenly among injured targets which means if only one target is injured, they will be receiving 100% of your Ancient Teachings healing which can cover decently high damage intake on one player. If there’s 2 injured players then you still may be able to get away with continuing your DPS rotation depending on how intense the damage is. At 3+ injured players I’m considering sending Sheilun's Gift or another cooldown if I can afford it.2. What kind of damage are they taking?
If they’re taking moderate to low damage, you can continue the DPS rotation and heal through Ancient Teachings . If the damage is more severe or sustained over a long period of time, it’s time to consider a cooldown like Life Cocoon for single target or two targets to help mitigate some of the casting required and again at 3+ if it’s moderate to heavy damage then send a stronger cooldown like Chi-ji. It's also important to note that Ancient Teachings and Aspect of Harmony will not heal full health allies even if they have a heal absorb on them.3. How many enemies can I hit?
Mistweaver scales slightly with multiple enemies to hit and as a result it can be a little more effort for similar throughput when there’s only one enemy to hit. This is most noticeable with Ancient Teachings but it can impact which spells we end up using to heal. You should be able to heal through Ancient Teachings better on multiple targets, but on single target you may need to consider casting depending on the intensity of the damage4. Do I need to specifically hold cooldowns for another mechanic? What cooldowns do I have available?
If you have significant healing to do but there’s unexpected damage taken, it’s time to consider which cooldowns you have available, and which ones will be back up before their regular use time. Usually this will end up being Sheilun's Gift or Jade Empowerment, since these have the shortest cooldowns and shortest use time (a one-time cast and a short channel).