None of them are. Every snippet I’ve seen for every inroad has your patron Master introduce you like a bad habit they can’t shake. And the last time I saw a snippet of Cups reacting to its almost-murderer in The Crocodile Who Would be King? It reacted to the player in pretty much exactly that fashion.
EDIT: There’s also the argument to be made that it would volunteer to send you to the roof in the hopes that you die permanently in the attempt.
Literally all that’s required in-story is a (grudgingly) cordial invitation, and a corresponding introduction. Both of which can be achieved conveniently with a hand mirror tapping a heads-up in Morse code.
EDIT: And could also be framed conveniently as a shock to Mr Mirrors’ former peers, who speculate that it inviting you might signal its first attempt to re-enter the game proper.
EDIT: You’d also think at least Pages would have noticed this: Ambition: Nemesis – One Last Matter - Fallen London Wiki