Short answer
No, mackerel isn't toxic, so urgent care isn't needed. For a one-time small portion, just watch for mild stomach upset like vomiting or diarrhea over the next 24 hours. Offer plenty of fresh water and skip the next meal if their stomach seems unsettled. Contact your own vet if any digestive issues last more than a day.
Mackerel — Food safety facts
Safe to share · Cats · full breakdown on the linked food page
Safe cooked, but it is oily — small occasional portions only.
The full verdict, portion guidance and serving notes are collected on the Mackerel food facts page.