Different companies have different policies but it is pretty standard to have to pay up front for warranty items being shipped to you, then getting a refund when you ship the item back to them.
Some companies (a lot, if not most) make you pay the return shipping, and some will issue a call tag on their account.
I personally wouldn't complain about paying shipping to me if they aren't requiring you to put up a deposit for the new part until they get the old one back.