It does show the correct quantity when logged in, logged in users never see a cached page.
Looking in to it, it might be a case of adding woocommerce_after_product_save as a hook to purge a specific post, but looking at the GitHub issue history there are some issues that seem to suggest it should already be working with Woo? Very odd.
If you don’t mind taking a look that’d be great, I’m happy to send you in private some URLs if you’d like to do some debugging, just didn’t want to post them on the forum publicly.