It is not necessary to create email aliases for your default email account, as your default (primary email account for the domain) acts as a "Catch All" account. In other words, "firstname.lastname@example.org" will be automatically be delivered to your default mail account.
To use aliases off other email accounts in your domain, go to your cPanel control panel, and under the Mail Menu heading select "Forwarders." Fill in the blanks (it's easy, you'll see when you get there.)
You may also use forwarders to forward email from any of your domain email accounts to other address/es.