Since this post is mostly about that red trinity there, I'll just explain that, even though I think you seem to know what's going on?
There are actually two trinities in the Manor Ruins (one is a Trinity Ladder, or either it was another red one, I honestly don't remember right now). One grants you access to a treasure chest, and one is just an indicator. The red trinity to the right of the fence is inaccessible (or at least it should be, as I had already completed all the trinities and gotten the trophy before I noticed the extra one).
If that red trinity is there when you enter that area, that means the robot heartless will not spawn, if it is not there then you should consider yourself lucky because you will have the chance to fight it and pick up at least one if not two Blazing Stones (rare synthesis item, you need a total of 7 if you plan on synthesizing everything for the trophy).
I wasn't aware that the indicator trinity was supposed to be there for you to grab that other trinity there though, I may have forgotten about it since I had done that beforehand. Which would make it (Red Trinity indicator shows up so you can grab the other trinity, but you can't fight the Chimera, as it won't spawn.)
Oh yeah, here's a neat trick for you to go by, when you have Encounter Plus equipped, all it takes is two rooms to reset the counter for a rare heartless to spawn, it's not always two times though. At minimum it will be 5 for the rarest heartless such as the Pink Agaricus.