I have other Gmail accounts and somehow they are all tied to my Brenau email account. It shows my mailto:xxxxx@tiger.brenau.edu as the default account with other Gmail accounts listed.

Gmail supports multiple accounts being logged in at one time so users can easily switch between them.
 
If this in confusing to you and you don't want to be logged into them simultaneously - just click on the email address in the top-right of the screen and choose "Log Out" which should log you out of all of the accounts.

We recommend you keep your accounts separated using "Profiles" which is explained here:

Helpdesk