To my understanding.
The mentor is a reincarnator and not Tristan.
Tristan and others got the play's script/game's plot information from the mentor.
They suspect/almost certain Cyril is also reincarnator, but both side are just throwing feints for now.
I think Tristan specifically calling for milk tea at the end was him dropping 'I know something' to Cyril, much like how Cyril tried to probe Chloe indirectly earlier (and Chloe, not being able to figure out 'what' Cyril was trying to learn, got impatient and just ask him)