You are correct. If the card has no Shadow Effect, he attacks, you apply the damage and then he returns to staging.
One of the few cards I actually HOPE there's a shadow card dealt so I can thwack him with a Glorfindel-Aragorn one two punch!
He's not correct. He's asking if Mountain Warg returns to the staging area BEFORE its attack resolves, which it doesn't because the wording on the card is identical to Wargs. Not sure what the OP is talking about.