When logs in Quote List page works which means reflects what has been added or deleted. If user is not logged in, user has to refresh the page to reflect the changes. Why?
It has several reasons, it could be caching or some settings in .htaccess.
In case of caching, you might be using some caching plugins like W3Total cache or any other host which implements caching like WPEngine. Please follow the instructions detialed out in the following uRL:
In case other settings like may be in .htaccess seetings like below:
I hope this post would really help you to fix the issue.