Azure SQL Database "Login failed for user" contained users.
It looks like you mixed a few different steps from the Azure article. Many of these Azure articles contain lots of great information but the layout is borderline horrible. Topics just blend into each other making it confusing for most readers (DB firewall configuration is another commonly confused doc).

If you want to use contained DBs with contained users, your create user statement should be something like

CREATE USER MyContainedUser01 WITH password='MyL@m3P@$$0rd';


as described in https://azure.microsoft.com/en-gb/documentation/articles/sql-database-manage-logins/#managing-contained-database-users

When you create a user mapped to a login as per your sample script, that's a regular, non-contained user. With that, you need to connect using the login which then maps to the user.