I was playing a house of M team last night and I had Quicksilver w/ Maneuver. The first HSS attack I rolled with him were doubles, thus causing knock back. So I understand that after the attack resolves implies that the knock back would be applied first, but this is where we were unsure, can Quicksilver still Maneuver? My argument was that the card's wording doesn't state that the character needs to be adjacent. It states that after the attack is resolved move the target in any adjacent square to the character. No where does it say the target needs to be adjacent. Am I correct on this?

Yes, you can use Maneuver if a character takes knock back from an attack.

Knock back happens before the attack is resolved so you the attacked character would knock back then you would place the character in a square that is adjacent to the attacker.