Customer sessions not ending

A client is reporting that when he visits his site, he's already logged into a customer account. This had happened twice to two different employees and two orders have been received under the wrong customer account indicating the same behavior. The customers reported the same behavior, having been logged in already.

The template was recently changed and this problem was not reported prior to that.

What would cause such behavior? COWOA is not installed, no master password plugins...it's not customized much at all. I'm hesitant to post the url until the issue is resolved.

Sure would like to have more of the info asked for in the posting tips. You can post your site as yoursiteDOTcom if you want to hide from the SEs.
One stab I might make at this is that you are using PayPal but not PayPal Express.

PHP Version 5.4.45
PayPal Express and PayPal Payments Pro are installed
url is ghostoutlet DOT com
No plugins are installed.