incompatible with browser caching turned on in incognito tab in chrome

If you use a plugin to leverage browser caching (e.g. I use WP Fastest Cache), and you are on the site in an incognito tab, login will succeed, but the page refresh will not show the user as being logged in.

I know it’s an edge case, but I’d like to try to find something that’ll make this work since it does work in a regular tab.