Ok. I have solved the issue. Single form does not allow to save custom fields to more than 1 location. You can save them either to post, or product, or… whatever.
So even though I am creating a post and a product in one form, if I save custom fields to a post, product category is not updated for the product.
I also see that the post is unable to read the data from product fields, and product is unable to read data from post field…
Some thought for the future release!