@Transactional annotation is not working

This code is about some database actions:

@Component("trans")
 public class CustomerTransactionImp extends JdbcDaoSupport{

    public static final Logger logger = Logger.getLogger(CustomerTransactionImp.class.getName());

    @Autowired
    public CustomerTransactionImp(DataSource dataSource) {
        setDataSource(dataSource);
    }

    @Transactional
    public void deleteCustomerByName(String name){
        String sql = "DELETE FROM CUSTOMER WHERE firstName = ?";

        deleteCustomerByID((long) 100);
        displayAllCustomer();
        logger.info("Deleted customer named: "+ name);
        getJdbcTemplate().update(sql,name);
    }

    public void deleteCustomerByID(Long ID) {
        String sql = "DELETE FROM CUSTOMER WHERE id = ?";

        logger.info("Deleted customer named: "+ ID);
        getJdbcTemplate().update(sql, ID);
    }

    public List getAllCustomer(){
        String sql = "Select * FROM customer";

        return getJdbcTemplate().queryForList(sql);
    }

    public void displayAllCustomer() {
        for (Object o : getAllCustomer()) {
            System.out.println(o);
        }
    }
}

This is my Spring configuration file:

<?xml version="1.0" encoding="UTF-8"?>
<beans xmlns="http://ift.tt/GArMu6"
       xmlns:xsi="http://ift.tt/ra1lAU"
       xmlns:context="http://ift.tt/GArMu7"
       xmlns:jdbc="http://ift.tt/18IIlo0" xmlns:tx="http://ift.tt/OGfeU2"
       xsi:schemaLocation="http://ift.tt/GArMu6 http://ift.tt/1jdM0fG http://ift.tt/GArMu7 http://ift.tt/1jdLYo7 http://ift.tt/18IIlo0 http://ift.tt/1b0hqjk http://ift.tt/OGfeU2 http://ift.tt/18tm2Tg">

    <context:annotation-config></context:annotation-config>
    <context:component-scan base-package="database.transactionmanagement"/>

    <jdbc:embedded-database id="dataSource">
        <jdbc:script location="sqlfiles/schema.sql"/>
        <jdbc:script location="sqlfiles/data.sql"/>
    </jdbc:embedded-database>

    <tx:annotation-driven transaction-manager="transactionManager"/>

    <bean id="transactionManager" class="org.springframework.jdbc.datasource.DataSourceTransactionManager">
        <constructor-arg name="dataSource" ref="dataSource"/>
    </bean>
</beans>

And my test class:

 @Test
public void trans_management_test() {
    ApplicationContext context = new ClassPathXmlApplicationContext("databaseconf/transaction-conf.xml");

    CustomerTransactionImp customerTransactionImp = context.getBean("trans", CustomerTransactionImp.class);

    customerTransactionImp.deleteCustomerByName("Omer");
    customerTransactionImp.displayAllCustomer();
}

So basic codes, in the code where I use the @Transactional annaotation, I created a wrong SQL query, the table is not my db-:

String sql = "DELETE FROM CUSTOMERWrong WHERE firstName = ?";

I mean, in the deleteCustomerByName method, here is deleteCustomerByID method and this method is working fine and commit.

According to transaction, deleteCustomerByID method must not commit or my understanding of the @Transactional annotation will be wrong. The SQL query under deleteCustomerByName method is wrong while the SQL query under deleteCustomerByID is okay, all of them must not commit???