Obviously review the dealer's policy. But yes, most dealers, and TW is not an exception, bill you when the item actually is in stock to them (arrived at their physical warehouse). Now, it also may take a day for them to process and physically ship the item and even then, imagine a big shipment of a trailerload of items going out- take more time for it to begin tracking in that shippers system.
Again, read your dealer's documentation and policies. You bought it from them, your sales contract is with them.
https://www.trainworld.com/ordering-policy
Back-Orders/Pre-Orders
Back-Orders and Pre-Orders are available for certain items that are not currently in stock as well as items that have not been released yet................ You will not be charged for the B/O items until we have received them from the manufacturer.