The processing fee comes first and is spent to be vetted. The gift follows only after vetting succeeds. Progression afterwards depends on the underlying EB-1 or EB-2 classification and on visa availability, neither of which the payment accelerates.
Paying is not the last step, and it is not the fastest one
The sequence matters because it determines what is at risk at each stage. Paying the per-person fee buys consideration, not approval, and a household of three has committed a meaningful sum before anyone knows the outcome. Making the gift comes later and is contingent on vetting having gone well, which is the programme's own safeguard against the worst version of the arrangement.
What follows the gift is ordinary immigrant processing through EB-1 or EB-2, subject to the monthly visa bulletin, and that stage moves at the speed the bulletin allows rather than at the speed a payment might suggest. Because the published terms of a new programme change, Anselm should re-read the official page at each transition rather than relying on what was true when he started, and he should not arrange his company's succession around a date the programme has not promised him.