Cyberzork gave me some steps to follow to fix the “same emails appearing in all accounts” problem.
You have to delete the account that isn’t showing correctly (this can be done in the Accounts menu option) and then re-add it again via the menu button->Accounts->Add Account
This will require you to log into your Yahoo account at the end (might need to use full @sky.com address) and accept the dialog which will be displayed to allow eM Client to access the Yahoo account.
The forum post is here: