Hi,
The quantity of the main product will update at the same time the quantity of the variant will update.
So the problem is probably that there is something missing in your tests.
For example, you have the "Update the product stock on confirmed status" setting in the HikaShop configuration.
If you have that option activated, then the stock will only be updated for the variant and the main product when the order status is changed from "created" to "confirmed" after the payment notification is received.
Also, the system bases itself on the settings in the menu System>Order statuses so if you changed things there it could prevent the stock update from being run.