I don’t usually work custom fields into admin hooks very often, so I would imagine that this is only happening to get_field() calls that exist in admin-side hooks (pre_get_posts for an example). Also not really familiar with how the plugin update process works, but I do know that the plugin folder is cleaned out and the new plugin is extracted, so the errors are probably firing somewhere between those two events.
Solution? No idea. Maybe just do your function_exists checks on the hooks and filters that apply to admin-side functions…
