Probably Not
I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.
Leomund's Tiny Hut states that:
Spells and other magical effects can’t extend through the dome or be cast through it
It would appear that A is magic, or at least magical.
Faezress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki
I would say that...
Depending on how the DM wants to rule it, they could say that the Faezress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.
Otherwise:
if the faezress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faezress, so the players would not suffer from madness