Hi emaistrellis
The total stock of all the inventories is not being summed to the original WooCommerce stock field. This original stock is being synced with the Main Inventory though.
Using the Multi-Inventory add-on, to get the stock of individual inventories you would have to obtain it from the wp_atum_inventory_meta table, except for the main inventory, that is saved by WooCommerce as a meta key in the wp_postmeta table.
I hope this helps.
Best Regards,
Salva.