It is definitely immigration first, then pick up bags. I haven't used them, but we did see at least one VIP service - not sure if it was this one https://vipservices.sx/ or this one, https://www.airsxm.com/vipservices or a different one. Like it says on the page, they had the passenger's name and met them at the arrivals before immigration and took them to the front of the line. For us, it would have only saved 5 or 10 minutes, but on a busy day, it would could help cut the time.