Before, where it is material. Once the person is already performing different work at a different site, the options narrow to explaining or correcting the position. The lead time depends on what the change is, so the review gate should sit at the point a change is proposed rather than when it is approved.
Build the gate into the project schedule
Delivery schedules rarely leave room for an immigration review, so the review has to be scheduled rather than fitted in. Agree a realistic turnaround with counsel and put it in the change-control process as a step with a duration. If a change genuinely cannot wait, decide the fallback in advance, usually keeping the person on the original scope until the review is complete.
There is a practical reason the gate belongs at proposal rather than approval. Once a change is approved, the project has committed dates and staffing to it, and a review that recommends waiting is then arguing against decisions already made. At proposal stage the same advice costs nothing.
Agree a standing turnaround with counsel, expressed in working days, and treat anything faster as a favour rather than a plan. Where a change genuinely cannot wait, the fallback of holding the person on the original scope preserves the position while the review is completed, which is almost always better than correcting it afterwards.