How do ESPs typically handle suppressions?

Most ESPs store suppressions at the account level. When you upload or send to a segment the ESP automatically removes suppressed contacts during the send process. Many ESPs also apply their own global suppression lists to protect the reputation of their shared IP pools. If one sender hits a spamtrap the ESP suppresses that address for all clients to prevent the entire fleet from being penalized. This happens behind the scenes like a quiet checkpoint that filters your manifest before the ship departs.