The data modeler doesn't have a 'live push' of generated SQL to a database. The main reason for this - this can be VERY destructive code. Alters, drops - all kinds of fun things.
You need to test that first.
So take your generated code and save it to a file or copy it, and then open it in your database tool of choice.
You say phpmyadmin - that's for MySQL. You should know that we don't have true support for MySQL in Oracle SQL Developer Data Modeler, just a generic ANSI SQL over a MySQL JDBC driver.
For full support of MySQL, you should use the MySQL Workbench - which will allow you to design and admin your MySQL databases.
I'm making this for my class and they recommend using Oracle 11g database
If you just need to design a schema/user, then you can get a copy of Oracle up and running very quickly. Either download and install Oracle Express Edition (XE) or get our Developer Day VirtualBox VM - which already has Oracle Database up and running.