It's not as simple as just announcing the borders are open....each country will have their own protocols, including Jamaica when it's announced the border will open here.
I'm sure you've read the Antigua Gov't protocols for international arrivals if you've made a decision to travel there in June...for those that haven't read it & might be curious...
masks are required in public, negative covid testing required 48 hours prior to travel, possibility of quarantining still....
https://ab.gov.ag/pdf/covid_news/Tra..._Protocols.pdf