Micro-managing the pet helps a fair bit, Adloquium is your mostly used heal, when it crits it puts a shield up for double the amount healed, otherwise it's just the amount healed.

Succor is best used when you know an AoE is coming up that can't be avoided, pair it with sacred soil if at all possible(unlike Adloquium it always shields for the amount healed).

As far as Eye for an Eye goes, it's honestly best used on trash, it's decent on bosses, but it shines on trash due to it being a proc and putting a debuff on anything hitting, in other words... Use it on cooldown on bosses, save it for large trash packs(Yay, WP speed runs) if not on a boss.

Physick is basically Cure, but mostly used to bring someone up to full health after using Adlo for the shield.

Sacred Shield is this nice little bubble you put on the ground that people can stand in and take less damage while it's up, use at your discretion(remember, it uses an Aetherflow stack...)

Lustrate is fucking amazing, I use it a fair bit, mostly to blast someone up, or to quickly top someone off, it also uses an Aetherflow stack.

Ressurection, Raise, learned later, always able to be used in battle.

Leeches, same as Esuna, but learned a hell of a lot later.

Virus, yay, boss does less damage.

Choosing which pet to use is up to you, they both cast embrace so little healing lost depending, Eos's Whispering Dawn and Fey Illumination are nice in case of emergency though.