Xavier,
Are you using the WooCommerce shipping zones for your own admin products?
The only shipping method that the vendors can use to set their own rates, and then have those rates applied at checkout, is the Vendor Shipping (wp admin > woocommerce > settings > shipping > vendor shipping).
As admin, you mark “use vendor shipping as a standalone method”. and then set default admin rates for the site.
Then, each vendor must set their store address (important) in the pro dashboard > settings > store, and then set their own rates in their pro dashboard > settings > shipping
The WooCommerce zones will not work properly for the vendor shipping- they will not be able to choose the rates and have them apply properly.