How Do I Get My Stormwaker Puppet To Cure Me?!

I'm very new to pup and want the whm puppet for soloing but for now I'm lvl 30 with the stormwaker and it seems to spam black magic and once in a while cure itself or use protect on me. But it has only ever cured me once. I have tried both the head and body stormwaker, just the head, or just the body. It's just alittle confusing and I'm assuming when I get the whm puppet I won't be able to choose what spells it uses and when it uses them.?

Maneuvers help determine the spells it prioritizes. Using a Light Maneuver will help you get the cures you desire, as will using a Damage Gauge.

Make sure you have Damage Gauge attachment on as well.

http://wiki.ffxiclopedia.org/wiki/Damage_Gauge

here you see the % of health when the pup can cure you, depending how many light maneuver youhave active and if you use the listed attchements

I have the damage gauge but I only had one or two light maneuvers on. But now, hoe does the soothsayer work? I'm assuming that I can't control what spells it uses? Whether it's pro/shell, or cures? Just the same thing with light maneuvers and damage gauge on and it will be random?

It's a priority system so it's not random. The wiki entry does a good job of explaining each head's priority structure. (here's Soulsoother Head)

So basically it has a predetermined order in which it will cast spells, and the use of maneuvers and certain attachments will switch around the priority. For example, deploying the auto with 1 light maneuever will force its first enfeebling spell cast to be Dia.