An email alias is simply a forwarding email address. The mail server simply forwards email messages addressed to an email alias on to another, the specified email address.
So in your case, when email is sent to firstname.lastname@exprealty.com, it automatically forwards to your personal email address. Since this is an alias, there is no login information needed as there is nothing to log into, other than your personal email address.
If you would like to send emails from your eXp account, you will need to use either a Gmail or Yahoo forwarding email address. Here are instructions on how to configure each email service to send as your eXp alias: