Wishlist doesn’t need your customers information and it is not necessary to login to use wishlist. It saves products in PHP session while customer visit your website. You can find more about the plugin on its official page https://yithemes.com/themes/plugins/yith-woocommerce-wishlist/
Got it that’s what I saw but I had two customers say they saved items then came back a few hours later and they weren’t in the wishlist anymore? Any idea why?