Lesser—Illusory Maestro (Su)
As a move action, the familiar’s master can transfer control of any illusion spell that requires concentration to the familiar. The familiar’s affinity for illusions also enhances the quality of the illusion, increasing the illusion’s save DC (if any) by 1 for as long as the familiar concentrates on the spell.
When an illusionist with an illusion school familiar transfers the spell to the familiar, who then controls it?
Let's take Major Image for example. Unless I've been doing it wrong, while the caster is concentrating on the spell they can have the image play out how they want (for example, illusory monsters can react to enemies). If the familiar is now the one doing the concentrating, does that mean it has to make the decisions? Like a cat familiar making a bunch of mice show up because it's hungry, or show images of dead dogs because of reasons?
It says "can transfer control," so I'm pretty sure the familiar now controls it and makes the decisions. In general I would expect the GM to let the player dictate the familiar's choices, though that's not actually required. But even a novice's familiar is pretty smart for an animal, and by the time you can cast major image it's certainly in human range, so I would think quite poorly of any GM who dictated that the familiar does something inappropriate to the situation such as your examples.
What's interesting about Illusory Maestro is that I belive it implies that the orginal caster can now go and cast *another* spell. Because Illusory Maestro's "transfer control" indicates that the wizards is now free of controlling the concentration-durationed spell.
In 3.5 D&D, there was a Skill Trick and a Feat that changed the control mechanism of the concentration-durationed spell to a different action type than Standard Action ... but still tethered the caster to the restriction of "You can’t cast a spell while concentrating on another one."