I don't know what Amazon specifically will do (didn't know they allowed international shipments to begin with!), but the customs process via any normal carrier is that you get a bill when your items arrive at the port of entry.

You pay the bill, the item is released, and you get it a few days later. FedEx, for example, does the whole thing online.

FedEx in my case paid the bill to customs, shipped me my item, and then secondary sent me a bill to pay for the customs fees after I had already received the item.

They don't want shipments stuck in port because storage there is expensive.