The popup has various options you can use to control how it behaves.This is by design - I am a single developer doing this on a voluntary basis, and haven't got time to be looking after sensitive user data, so I've gone around the problem by avoiding contact with it altogether.
The cookies that are set by Amazon enable queries sent by the extension to succeed, but the extension doesn't look at those cookies, store them, share them or misuse them in any way. The extension never sees your log-in credentials - you supply them directly to the Amazon page. You may disagree and be able to navigate around your amazon stuff directly, but the warning has been generated because the site has responded to the extension's queries in a way that suggests that for at least some queries a log-out and log back in will help. Sometimes, the extension will warn you you're logged out.The more orders you have, the longer it takes. At some point it will clear the amazon window and place an orange progress bar that grows until scraping is complete. The extension updates scrape query statistics in the pop-up, so you can see how the fetching/scraping is progressing. Click on one of the year buttons to scrape and display a year's worth of orders.Click on the extension's icon (orange A) bringing up its pop-up/control panel.Navigate to one of the supported amazon sites, and make sure you're logged in to your amazon account on that page (so that the extension will be able to see your account data).This should permanently display the extension's orange A (for amazon) icon in your extension bar. (Optional) pin the extension icon in your browser by clicking on the jigsaw puzzle piece icon (high right in the chrome browser window), and then clicking on the pin next to "Amazon Order History Reporter", making the pin icon blue.