The product inventory is not being updated correctly after changing the stock levels in Atum, but only on the front-end of the website when viewed on mobile. If I go into the actual product listing in Woocommerce and update it from there it displays on the website correctly. Looks like inventory changes made via Atum are not urging the mobile cache to change. Desktop version of the site is behaving fine.
update: upon further investigation it seems that the desktop version of the site is not being updated also. Support from my hosting provider (Rocket) said this:
"It looks like the plugin is not sending a call to clear the cache when the changes are made. This is something we can't change from our side, actually, so you'd need to check with the plugin team what their orientation would be on that case.
If there is anything we can do from our side, like excluding a cookie from being cached, we can surely help, but our system is already set to automatically clear CDN Cache whenever a change is made(And this is why it saves when you change via WooCommerce directly), so if it is not changing, it means that the plugin is not running a command to clear the cache."