funny how i can see your reply on chrome but not on mozilla...
I dont think it's possible to sign out of the actual App. When inside the App's "home page" (where you'll see the timeline, mentions, direct message etc.) there is a button on the top left <Accounts>, clicking that brings you to the page that previously had 2 accounts: mine and his. Swiping the accounts doesnt bring up the delete button (like in notes, email etc) and neither does clicking them (just brings you back to "home page". The "edit" function on the <Accounts> page only allows reordering of accounts, not a delete function.
So i assume the only way of "signing out" is to delete his account in Settings > Twitter > "Username" > Delete Account.
Thanks for the quick response.