It was so annoying yesterday while trying to sign out of the Twitter app on my iPad 3 running iOS 8.4. I couldn’t find anywhere to tap for me to log out of my account. After googling it, I was able to discover that I have to remove my Twitter account via the iPad “settings”.
To remove your Twitter account,
==> Tap the “Settings” app
==> Tap “Twitter”
==> Tap on the account you want to remove
==> Tap “delete account”
==> Launch the Twitter app
==> Tap on “Me”
==> Tap on the round settings icon under your Twitter header image
==> Tap on “Sign Out”.
If you’ve added multiple Twitter accounts to the app, select the account you want to log out from the “accounts” icon next to the “edit profile” tab when you navigate to the “Me” tab of the Twitter app.
This method might still revert you back to the first method. So, the first method is highly recommended.
I hope this helps.