After having investigated the issue, we've concluded that it isn't a bug.
1) There are quantities in variable product, but it's shown out of stock in "Products" page of Woocommerce.
When you enable the "Manage Stock" at variable level and leave it at "0" makes WooCommerce understand that the product is out of stock. So, we recommend having Manage Stock at the variable level deactivated and activating and managing it at the level of the variation.
2) So, I did Bulk edit > Manage stock > No in Woocommerce Products list page. The problem solved temporarily.
Please, follow our recommendation above.
3) When I enter stock 0 for Quantity in ATUM, the product is still showing in stock in "ATUM STOCK INDICATOR"
When this happens, if you refresh the page again, it will show correctly. This is because ATUM performs the calculations asynchronously. This is done this way in order not to affect performance and the data that hasn’t been modified yet.
4) There's no proper sync of stocks. i.e ATUM is not controlling Woocommerce quantity effectively
What is not synchronizing well, please? Could you give us an example?