Short answer
Monitor your cat for the next 24 hours for vomiting, diarrhea, or signs of choking like gagging. Your vet likely checked for any obstruction from the spiky skin and ensured the toxic seed wasn't ingested. If your cat is eating normally and seems comfortable, recovery should be straightforward; call your vet back if any new symptoms appear.
Rambutan — Food safety facts
Feed with care · Cats · full breakdown on the linked food page
Flesh only and only a little. The seed is toxic and the spiky skin is a choking risk.
The full verdict, portion guidance and serving notes are collected on the Rambutan food facts page.