If the target is missing under 200 HP while the necessary amount of Light Maneuvers to trigger a Cure spell are active, the automaton's default cure spell will be Cure IV instead of Cure V.
At 99 Cap, with appropriate Automaton Magic Skill, will have access to Cure VI, which, as written above, will only be used if Cure V isn't enough to get the target to ~95% health (more testing needed to find the exact trigger). It appears the default Cure is Cure V while Cure VI is used for "Dire Circumstances" (Cure V via the Soulsoother Head is more mana efficient, as Cure VI via the puppet doesn't ever seem to hit the numbers a WHM can)
If unable to cast the highest tier spell (Cure VI, Protect V, Shell V, Poison II) the automaton will cast the highest tier spell possible depending on skill and mp.
With one active light maneuver, automatons will prioritize HP recovery over curing status ailments. Automatons will also prioritize HP recovery when HP level is extremely low.
It will cure the master and puppet first, prioritizing whoever has more hate. It will then prioritize whichever party member has the most hate. Healing and -na spells on party members requires a light and water maneuver respectively. Cures only occur when below a certain percentage of health. For more information on the health percentages that influence curing priority, see the Damage Gauge article. Status removal will be prioritized over curing, regardless of maneuvers or other triggers.
Regen will be cast on the party member (including the automaton) with hate when their HP is high. Regen will only be cast when the master, puppet or party member is fighting a mob within five levels below the target's level or higher . Regen is cast based on the spell targets level versus the mobs level, so if in a party where the mob checks as too weak to the master but Even Match to another member the puppet will cast regen on that member but never on the master.
There is no known maneuver that will trigger regen.
The automaton will not cast spells on alliance members, adventuring fellows, other pets or quest NPC's.