I'm necroing the thread for posterity, in case someone comes up with an official answer to what seems currently to be a a bug with the scenario -which oddly hasn't been brought up anywhere earlier in the thread.
Current scenario says: "If Giles Halmis is undefeated,a random other character who has not encountered him this turn summons and encounters him.
If Giles Halmis is defeated, or if all other characters have encountered him this turn, banish him. Then continue your encounter with Vakarla the Wrecker."
The above obviously doesn't address the case where Giles is EVADED - which by current RAW would not summon more copies of him and could therefore block the active character from proceeding with his Vakarla encounter (ex. Character A encounters Vakarla, character B summons and evades Giles - but there's also a Character C who has not -and will not- encountered Giles. So Giles will never be encountered by all characters besides char. A, nor will he be defeated.)
The two possible intents are:
"If Giles Halmis is undefeated or evaded..."
"If Giled Halmis is defeated, evaded, or if all other characters have encountered him..."
Hopefully, at some point, someone official can stumble upon this and give an answer.