The processing fee comes first, vetting follows, and the gift is made after vetting rather than before it. An instruction to send the large sum ahead of that sequence does not match the published order and should stop the process rather than accelerate it.
Sequence is a safeguard, so keep it
The order is not administrative housekeeping. It exists so that the substantial payment is made once the applicant has been examined, and reversing it puts the whole sum at stake before anyone has established that the applicant can proceed at all. Hypothetical example: a household near Saint-Joachim-de-Shefford is told by an intermediary that a place can be reserved by transferring the gift immediately, with vetting to follow, and that the offer closes on Friday.
Every element of that is wrong in a recognisable way: it inverts the published sequence, invents a deadline and introduces a party the official instructions do not mention. Two rules make this simple to police. Follow the sequence the official page sets out, and confirm the destination of any payment from that page rather than from an email, however well produced the letterhead.
If an intermediary's instruction differs from the official instruction, the intermediary is wrong, and slowing down costs nothing that cannot be recovered.