Outlook considers each of your accounts separately.  You have a Calendar account that points to plantsciences Exchange server, and an E-Mail account that points to the mail.ucdavis.edu servers on campus.  Under Tools - Account Options, you'll see both of these listed in order of priority.  Click once on the email account to highlight it, then click the up arrow (in the toolbar near the right) to move it above the calendar account.

This will force your emails to use, as a default, the email account settings <username>@ucdavis.edu.

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In context, this makes more sense.  If you're using Outlook to check multiple email accounts, say your Google Mail, your UC Davis mail, and your Yahoo mail, then at work, your Outlook settings should have your UC Davis mail account at the top.  This way, all mail sent from work will use the @ucdavis.edu extension.  If you're at home, you might move Google mail to the top, so your email has the @gmail extension by default.

You can change the account for a particular e-mail you wll be sending without moving the main settings.  When you begin to write a new email, to the write of the address lines is the "Account" button.  Click on that and choose what you want your address to be.  If you're sending work email from home, click "Account" and choose your mail.ucdavis.edu account for that email.