While the
Cult Demagoge and the
Mindwitch are alive, the
Dark Commune is a
Psycher Character unit. This is because a unit has a whole is considered to have all the keywords of any model in the unit per the Core Rules.
Some units can include models that have different keywords. While a unit has models with different keywords, it is considered to have all the keywords of all of its models, and so is affected by any rule that applies to units with any of those keywords. If a rule only applies to models with a specific keyword, then it instead only applies to models in such a unit that have the correct keyword
Note that as soon as either of these two models dies, the
Dark Commune is no longer a
Psycher Character.