To add why managing Eos is important,

Whispering Dawn should always be used with Rouse and, if possible, also Fey Illumination. Eos will squander Whispering Dawn other wise at the start of any engagement.
Speaking of Fey Illumination, only Eos, another healer, and yourself will benefit from it as it increases cure potency, so don't concern yourself trying to buff the entire party with it.
While important in both manual control and auto, if you do choose to keep Eos in auto, Make use of pet commands Place and Heel. Placing Eos in key points for buffs allows you to stay out of potential danger from enemy AoE and allows you more mobility. Place becomes very important in certain dungeons and raids. Heel Eos when you need to move after the battle or else she will desummon if you leave her too far behind.

I can't offer much advice on Selene, I've only ever used her when I solo and leave her in auto.