From the Custom Fields > Updates screen, the “Update Plugin” button links to the current site’s plugin page. This is valid – the plugin appears from the search query – but the update prompt does not appear here in multisite mode, only in the Network Admin. This is confusing as I would expect the destination to either update the plugin upon landing or provide a link to do so.
My suggestion would be to update the file advanced-custom-fields-pro/pro/admin/views/html-settings-updates.php, line 92 or so, to use network_admin_url() instead of admin_url(). This will generate a network admin link in multisite mode and a current-site link in single-site mode.
For reference, here is what the queried plugins page looks like currently, and what it looks like in the network admin:
Current: https://ibb.co/vX9hTNT
With network_admin_url(): https://ibb.co/PwR30J4
System specs:
macOS 10.13.6
WordPress 5.1.1
Advanced Custom Fields PRO 5.7.10