Follow these extra steps to enable quantity sync for your WooCommerce store.
Next is to login to your WooCommerce Page and you must enable Inventory management in WooCommerce Product settings.
To bulk edit your products you will need to Enable Stock Management.
Set your desired stock quantity here as shown on this screenshot below.
Then for every variation, you will need to enable stock management. To do it they will need to go to Variations Edit panel for every product, tick "Manage stock?" and set the desired quantity.
Note: After enabling Manage Inventory/Stock products quantity will decrease the stock quantity after each purchase/order is made.