After, and only after the official terms have been verified on the day of payment. The program's stages set when the processing fee and the gift are due; nothing else about the couple's plans should drive an irreversible payment.
The payment stages belong to the program; the decision belongs to the couple
The official page describes the stage at which the processing fee is paid and the stage at which the gift is paid. Those stages, not the couple's moving plans or a realtor's timeline, determine when money is due. Before the first payment the couple should have settled the questions that the terms leave to them: whether to proceed on the family terms as written, whether the Canadian tax on the herd and quota sale has been provided for, and whether they are content that the gift is not recoverable.
If the couple also holds or is considering any other status, they should check from the official material whether the program addresses that and sequence accordingly. Set no date for the move until the application's outcome is known, and keep every deposit on U.S. housing refundable until then.
A pause costs nothing; a payment made on an assumption cannot be undone.