From what has been gathered thus far, it has appeared where intense bouts of negative emotion have occurred- the act of death, primarily. The apartments where Dia was killed, down by the river were Eliza was discovered, and likely the dollhouse where Chiaki and Seraphina experienced several deaths.

[He studies the new spot in the door as he continues.]

This is the first outlier. As you said, Dahlia, this doesn't seem to have spilled out from inside and was left as a remnant. But from what, I wonder? What was the purpose of attacking this door?

[...may as well throw another hypothesis out there.]

Perhaps the this door was locked for other reasons than to simply keep us out?