After experiencing LTE, 3G does feel like molasses. Lol. Just use WiFi and 3G feels not worth it.
With regards to US tourists, any phone not sold directly from manufacturers unlocked says 4G even when on 3G. There's no distinction between 3G/H/H+. 4G LTE or 3G is all they see. So all they may know is 4G in Jamaica is slow at times. As is the same issue when they're in US, but less likely to be experienced.
As for going to Digi or Flow as a visitor, I didn't know such problems existed. They ask for ID and where you're staying best I know.
In the other direction, not too many people I know use data while in US. Either they borrow a SIM from a resident or just don't use phone much at all. Wait for WiFi and use WhatsApp etc.