It's like a rogue; they can't cast spells themselves, but they can study magic well enough to trigger scrolls and wands and such. Keep in mind, my assertion that they should lose all spellcasting is only under the premise that they can attach castable spells to their puppets (the puppets would essentially be like sorcerers, in that they have a limited number of spells per day, and a limited set of spells they can cast from... but they would be EX abilities or SLAs, depending on the way you decided to take the class). At max level, this would essentially give the puppet master up to 15 spells to cast through his puppets... which is less than a Sorcerer at max level, but he can also cast up to 5 spells per round (as the class is currently written), which makes up for his lack of on-call versatility. Though during his down time, he could take a scroll and tinker with his puppet and replace one of the spells with the spell on the scroll, essentially giving them the ability to change their "loadout" ad infinitum.
For the record, I said 4:1 ratio because you're giving up 1 set of actions for 5 sets of actions, which is a 400% increase in action economy. Though I may have used the wrong term originally to express myself, thus the confusion.