Short answer
No, only the cat that ate it needs monitoring. Cooked taro is safer than raw, but it can still cause mild stomach upset in some pets. Watch your cat for drooling, vomiting, or loss of appetite over the next few hours. If you see any of these signs, contact your veterinarian for advice.
Taro — Food safety facts
Feed with care · Cats · full breakdown on the linked food page
Must be thoroughly cooked — raw taro contains calcium oxalate crystals that burn the mouth and throat.
The full verdict, portion guidance and serving notes are collected on the Taro food facts page.