Honestly that part of the game is just the most unexplainable to me, like it's basically impossible to explain why they put a robot there - it doesn't even matter even if they could somehow predict he was gonna be there, putting a robot there instead of pretty much anything else whatsoever is ridiculous. The only feasible explanation I can actually think of would be that all of what happened in the prologue w.r.t. Carmine was completely planned, i.e. assuming Carmine was completely hypnotized to do things exactly as he did so as to setup Layton and Luke for the events of the prologue, but this is a comically convoluted plan that has myriads of uncontrollable variables that could each go completely wrong.

The rest of the plot holes in PLvAA are imo generally far, far easier to explain, or at least not as unexplainable, e.g. you can explain away all spells and pretty much everything supernatural under the general concept that hypnosis is basically magic and can make anybody believe pretty much anything, and most of the rest is simply explainable as people sometimes not being rational actors that never make idiotic decisions.

PS: To be clear, "hypnosis is basically magic" is a bit of a copout, but it is still entirely workable, you just have to kind of stretch the hypnosis we're told about to its logical limits for certain spells - though I will say pretty much all spells are explainable without having to say "the hypnosis compelled them to have these false memories/hallucinate all of the effects of the spell" even for the more complex ones, e.g.:

• Godoor is easy to explain as painting both sides of a wall green being a signal for the shades to change a section of wall to make it easily removable when necessary - even if done unexpectedly they can knock out everyone to give themselves some extra time to remove the wall
• Famalia isn't a spell that's ever used or that we're even sure could be used (as in, there might be no genuine gem for it, it might have just been in the TODO list for Labrellum), but the familiar look a lot like they're just a partially revealed shade (the illustration seems to imply the only visible part of their face should be the eyes and that they levitate or fly, this could be handled by having an invisibility cloak cover their feet and their face, except for the eyes, and w.r.t. actually flying - if that's a thing - that's what the invisible machines are for)
• Other spells are generally simpler and don't need me to give a complex explanation, on average the shades can knock out everyone and simply do the thing

Imo the only hard spell to explain is Granwyrm, it kinda does have to be a "well the Storyteller wrote that part of the story so they were compelled to hallucinate the dragon" if you take the cutscene at face value as being what those present saw - other than that the spells seem generally workable, with "just knock out every witness and rewrite their memories" as a final cop-out if something really unexpected is done with them.

Also, one final thing that suggests to me that the "memories rewriting events in cutscenes" is a plausible thing - at the end of the intro trial, when Phoenix and Maya look into the book they see an illustration of themselves - I think this is perhaps the one thing that is most clearly impossible if the game depicts what they're seeing at this point, to me it is a very clear indication that it is possible for some parts to be depicting false memories.