Who pays the carriers?
One thing is the cost charged to the buyer, and another thing is what you pay to the carrier.
In this sense, the buyer buys and pays you, and you are the one who sells both the transport service and the product. It is you who will have to notify the carrier and manage the delivery as you consider best. You incur transportation costs regardless of what you charge your customer... which you will have to pay to the appropriate carrier.
The transport company you choose to deliver your products is decided by you at all times and the buyer only knows how much he has to pay for transport.
In short, and by way of summary, the transport configurations that you associate to your products are used so that the buyer knows how much he has to pay (for the product and for transport). As a seller you will have to make sure that the transport configurations that you have implemented correspond to reality and have agreed with the carriers the same price that you publish in your transport configurations. Once you receive an order, you will be the one who has to contact the carrier.