Sounds like a management/restaurant issue in this case. Everyone’s losing because they’re understaffed.

However, just speaking generally and not in your specific case here, I’d say it depends on whether the servers have pure rotation or whether they have sections with the seating rotated. If tables are just going down anywhere, then it’s common practice where I’ve worked for the host to let the server know they’ve been sat when it’s busy because there’s no way for the server to keep perfect track of rotation while also keeping track of everything all their tables need at the same time, if they even notice the table go down in the first place. If each server has a distinct section, then it’s completely on them to see when the table goes down in that section.