I use both WP-Listers (for Amazon and eBay) to sync stock and sales. I noticed that both WP-Listers ignore Multi-Inventory combined stock quantity and use only values from Main Inventory.
I've been informed that this has been previously resolved with the use of hook delivered by ATUM. Here's the question from WP-Listers support:
if there's anything we need to add to this:
// Adding support for ATUM Multi Inventory #37394
add_filter( 'atum/multi_inventory/bypass_mi_get_stock_quantity', '__return_false');
$stock = is_callable( array( $product, 'get_stock_quantity' ) ) ? $product->get_stock_quantity() : $product->get_total_stock();
remove_filter( 'atum/multi_inventory/bypass_mi_get_stock_quantity', '__return_false');