The true reality from someone who works in this space is that every company with an intelligent marketing department uses an email service specialized to help market to a customer file filled with email addresses with preferences tailored to each customer, and marketing campaigns are designed days or weeks in advance and scheduled to go out on a rolling basis. Email addresses that get queued up for some sort of email campaign are already "locked and loaded" to some degree and are not designed to be unraveled to remove one random unsubscribe request. Since the email providers receive client updates perhaps once a day to fill campaign lists, your unsubscribe as a rule will not immediately sync to be removed from any future campaigns you're not already signed up to receive. On top of that, syncs can and do fail, however infrequently. This means that if there is a technical issue with the connection of some sort, it can take a day or two to resolve. A heavy marketer may still send a couple emails to a customer that unsubscribed while that sync issue is being repaired.

tl;dr: Most companies remove you from email campaigns within a day. 7-10 days is CYA language in case something goes wrong.