Using the Plesk demo at http://support.hostgator.com/articles/plesk/demos-for-plesk I can see that their login form is responding to the “change” event that Kee triggers after performing an auto-fill by triggering a form submission.
So this appears to be a bug with the website or its libraries. Exactly where the problem lies might be easier to establish if we can find any other examples of this behaviour.
This is the stack trace from the form submission request:
I think that in this specific case, disabling auto-fill (not just auto-submit) on this KeePass entry will workaround the issue.