We process most requests within 24 hours. Some requests are processed in "batches" and sent to certain mailers 1x per month.
Once your request has been processed, it can take 8-12 weeks to see the mail completely stop.
This is because most mailers pre-print and distribute an additional 1-3 "waves" of their campaign upfront, to save on printing and distribution costs.
This "lag" time is typical of most mailers, and is the same if you opt-out of a mailer by contacting them yourself.